Sampling from a quantum distribution can be exponentially hard for classical computers and yet could be performed efficiently by a noisy intermediate-scale quantum device. A prime example of a distribution that is hard to sample is given by the output states of a linear interferometer traversed by N identical boson particles. Here, we propose a scheme to implement such a boson sampling machine with ultracold atoms in a polarization-synthesized optical lattice. We experimentally demonstrate the basic building block of such a machine by revealing the Hong-Ou-Mandel interference of two bosonic atoms in a four-mode interferometer. To estimate the sampling rate for large N, we develop a theoretical model based on a master equation that accounts for particle losses, but not include technical errors. Our results show that atomic samplers have the potential to achieve quantum advantage over today's best supercomputers with N≳40.
We demonstrate a method for determining the three-dimensional location of single atoms in a quantum gas microscopy system using a phase-only spatial light modulator to modify the point-spread function of the high-resolution imaging system. Here, the typical diffracted spot generated by a single atom as a point source is modified to a double spot that rotates as a function of the atom's distance from the focal plane of the imaging system. We present and numerically validate a simple model linking the rotation angle of the point-spread function with the distance to the focal plane. We show that, when aberrations in the system are carefully calibrated and compensated for, this method can be used to determine an atom's position to within a single lattice site in a single experimental image, extending quantum simulation with microscopy systems further into the regime of three dimensions.
We present a scheme to directly probe the Wigner function of the motional state of a neutral atom confined in an optical trap. The proposed scheme relies on the well-established fact that the Wigner function at a given point (x,p) in phase space is proportional to the expectation value of the parity operator relative to that point. In this work, we show that the expectation value of the parity operator can be directly measured using two auxiliary internal states of the atom: parity-even and parity-odd motional states are mapped to the two internal states of the atom through a Ramsey interferometry scheme. The Wigner function can thus be measured point-by-point in phase space with a single, direct measurement of the internal state population. Numerical simulations show that the scheme is robust in that it applies not only to deep, harmonic potentials but also to shallower, anharmonic traps.
Quantum speed limits set the maximal pace of state evolution. Two well-known limits exist for a unitary time-independent Hamiltonian: the Mandelstam-Tamm and Margolus-Levitin bounds. The former restricts the rate according to the state energy uncertainty, while the latter depends on the mean energy relative to the ground state. Here we report on an additional bound that exists for states with a bounded energy spectrum. This bound is dual to the Margolus-Levitin one in the sense that it depends on the difference between the state's mean energy and the energy of the highest occupied eigenstate. Each of the three bounds can become the most restrictive one, depending on the spread and mean of the energy, forming three dynamical regimes. We analyze these regimes and show they are accessible in a multi-level system.
High-bandwidth, fiber-based optical cavities are a promising building block for future quantum networks. They are used to resonantly couple stationary qubits such as single or multiple atoms with photons routing quantum information into a fiber network at high rates. In high-bandwidth cavities, standard fluorescence imaging on the atom-cavity resonance line for controlling atom positions is impaired since the Purcell effect strongly suppresses all-directional fluorescence. Here, we restore imaging of ^{87}Rb atoms strongly coupled to such a fiber Fabry-Pérot cavity by detecting the repumper fluorescence which is generated by continuous and three-dimensional Raman sideband cooling. We have carried out a detailed spectroscopic investigation of the repumper-induced differential light shifts affecting the Raman resonance, dependent on intensity and detuning. Our analysis identifies a compromise regime between imaging signal-to-noise ratio and survival rate, where physical insight into the role of dipole-force fluctuations in the heating dynamics of trapped atoms is gained.
Fabry–Perot interferometers have stimulated numerous scientific and technical applications ranging from high-resolution spectroscopy over metrology, optical filters, to interfaces of light and matter at the quantum limit and more. End facet machining of optical fibers has enabled the miniaturization of optical Fabry–Perot cavities. Integration with fiber wave guide technology allows for small yet open devices with favorable scaling properties including mechanical stability and compact mode geometry. These fiber Fabry–Perot cavities (FFPCs) are stimulating extended applications in many fields including cavity quantum electrodynamics, optomechanics, sensing, nonlinear optics and more. Here we summarize the state of the art of devices based on FFPCs, provide an overview of applications and conclude with expected further research activities.
Optical spectroscopic sensors are powerful tools for analysing gas mixtures in industrial and scientific applications. Whilst highly sensitive spectrometers tend to have a large footprint, miniaturized optical devices usually lack sensitivity or wideband spectroscopic coverage. By employing a widely tunable, passively stable fiber Fabry-Perot cavity (FFPC), we demonstrate an absorption spectroscopic device that continuously samples over several tens of terahertz. Both broadband scans using cavity mode width spectroscopy to identify the spectral fingerprints of analytes and a fast, low-noise scan method for single absorption features to determine concentrations are exemplary demonstrated for the oxygen A-band. The novel scan method uses an injected modulation signal in a Pound-Drever-Hall feedback loop together with a lock-in measurement to reject noise at other frequencies. The FFPC-based approach provides a directly fiber coupled, extremely miniaturized, light-weight and robust platform for analyzing small analyte volumes that can straightforwardly be extended to sensing at different wavelength ranges, liquid analytes and other spectroscopic techniques with only little adjustments of the device platform.
Quantum mechanics sets fundamental limits on how fast quantum states can be transformed in time. Two well-known quantum speed limits are the Mandelstam-Tamm and the Margolus-Levitin bounds, which relate the maximum speed of evolution to the system’s energy uncertainty and mean energy, respectively. Here, we test concurrently both limits in a multilevel system by following the motion of a single atom in an optical trap using fast matter wave interferometry. We find two different regimes: one where the Mandelstam-Tamm limit constrains the evolution at all times, and a second where a crossover to the Margolus-Levitin limit occurs at longer times. We take a geometric approach to quantify the deviation from the speed limit, measuring how much the quantum evolution deviates from the geodesic path in the Hilbert space of the multilevel system. Our results are important to understand the ultimate performance of quantum computing devices and related advanced quantum technologies.
The mapping of the potential landscape with high spatial resolution is crucial for quantum technologies based on ultracold atoms. However, the imaging of optical dipole traps is challenging because purely optical methods, commonly used to profile laser beams in free space, are not applicable in a vacuum. In this work, we demonstrate precise in situ imaging of optical dipole traps by probing a hyperfine transition with Ramsey interferometry. Thereby, we obtain an absolute map of the potential landscape with micrometer resolution and shot-noise-limited spectral precision. The idea of the technique is to control the polarization ellipticity of the trap laser beam to induce a differential light shift proportional to the trap potential. By studying the response to polarization ellipticity, we uncover a small but significant nonlinearity in addition to a dominant linear behavior, which is explained by the geometric distribution of the atomic ensemble. Our technique for imaging of optical traps can find wide application in quantum technologies based on ultracold atoms, as it applies to multiple atomic species and is not limited to a particular wavelength or trap geometry.
Transforming an initial quantum state into a target state through the fastest possible route—a quantum brachistochrone—is a fundamental challenge for many technologies based on quantum mechanics. Here, we demonstrate fast coherent transport of an atomic wave packet over a distance of 15 times its size—a paradigmatic case of quantum processes where the target state cannot be reached through a local transformation. Our measurements of the transport fidelity reveal the existence of a minimum duration—a quantum speed limit—for the coherent splitting and recombination of matter waves. We obtain physical insight into this limit by relying on a geometric interpretation of quantum state dynamics. These results shed light upon a fundamental limit of quantum state dynamics and are expected to find relevant applications in quantum sensing and quantum computing.
We present three high finesse tunable monolithic fiber Fabry-Perot cavities (FFPCs) with high passive mechanical stability. The fiber mirrors are fixed inside slotted glass ferrules, which guarantee an inherent alignment of the resonators. An attached piezoelectric element enables fast tuning of the FFPC resonance frequency over the entire free-spectral range for two of the designs. Stable locking of the cavity resonance is achieved for sub-Hertz feedback bandwidths, demonstrating the high passive stability. At the other limit, locking bandwidths up to tens of kilohertz, close to the first mechanical resonance, can be obtained. The root-mean-square frequency fluctuations are suppressed down to ∼2% of the cavity linewidth. Over a wide frequency range, the frequency noise is dominated by the thermal noise limit of the system’s mechanical resonances. The demonstrated small footprint devices can be used advantageously in a broad range of applications like cavity-based sensing techniques, optical filters or quantum light-matter interfaces.
Elementary building blocks for quantum repeaters based on fiber channels and memory stations are analyzed. Implementations are considered for three different physical platforms, for which suitable components are available: quantum dots, trapped atoms and ions, and color centers in diamond. The performances of basic quantum repeater links for these platforms are evaluated and compared, both for present-day, state-of-the-art experimental parameters as well as for parameters that can in principle be reached in the future. The ultimate goal is to experimentally explore regimes at intermediate distances - up to a few 100 km - in which the repeater-assisted secret key transmission rates exceed the maximal rate achievable via direct transmission. Two different protocols are considered, one of which is better adapted to the higher source clock rate and lower memory coherence time of the quantum dot platform, while the other circumvents the need of writing photonic quantum states into the memories in a heralded, nondestructive fashion. The elementary building blocks and protocols can be connected in a modular form to construct a quantum repeater system that is potentially scalable to large distances.
We report on vibrational ground-state cooling of a single neutral atom coupled to a high-bandwidth Fabry-Pérot cavity. The cooling process relies on degenerate Raman sideband transitions driven by dipole trap beams, which confine the atoms in three dimensions. We infer a one-dimensional motional ground-state population close to 90% by means of Raman spectroscopy. Moreover, lifetime measurements of a cavity-coupled atom exceeding 40 s imply three-dimensional cooling of the atomic motion, which makes this resource-efficient technique particularly interesting for cavity experiments with limited optical access.
We demonstrate the storage of 5 ns light pulses in a single rubidium atom coupled to a fiber-based optical resonator. Our storage protocol addresses a regime beyond the conventional adiabatic limit and approaches the theoretical bandwidth limit. We extract the optimal control laser pulse properties from a numerical simulation of our system and measure storage efficiencies of (8.1±1.1)%, in close agreement with the maximum expected efficiency. Such well-controlled and high-bandwidth atom-photon interfaces are key components for future hybrid quantum networks.
We propose a realistic scheme to construct anomalous Floquet Chern topological insulators using spin-1/2 particles carrying out a discrete-time quantum walk in a two-dimensional lattice. By Floquet engineering the quantum-walk protocol, an Aharonov-Bohm geometric phase is imprinted onto closed-loop paths in the lattice, thus realizing an abelian gauge field—the analog of a magnetic flux threading a two-dimensional electron gas. We show that in the strong field regime, when the flux per plaquette is a sizable fraction of the flux quantum, magnetic quantum walks give rise to nearly flat energy bands featuring nonvanishing Chern numbers. Furthermore, we find that because of the nonperturbative nature of the periodic driving, a second topological number—the so-called RLBL invariant—is necessary to fully characterize the anomalous Floquet topological phases of magnetic quantum walks and to compute the number of topologically protected edge modes expected at the boundaries between different phases. In the second part of this article, we discuss an implementation of this scheme using neutral atoms in two-dimensional spin-dependent optical lattices, which enables the generation of arbitrary magnetic-field landscapes, including those with sharp boundaries. The robust atom transport, which is observed along boundaries separating regions of different field strength, reveals the topological character of the Floquet Chern bands.
We employ active feedback to stabilize the frequency of single photons emitted by two separate quantum dots to an atomic standard. The transmission of a rubidium-based Faraday filter serves as the error signal for frequency stabilization. We achieve a residual frequency deviation of <30 MHz, which is less than 1.5% of the quantum dot linewidth. Long-term stability is demonstrated by Hong-Ou-Mandel interference between photons from the two quantum dots. Their internal dephasing limits the expected visibility to V = 40%. We observe V_{lock} = (41±5)% for frequency-stabilized dots as opposed to V_{free} = (31±7)% for free-running emission. Our technique reaches the maximally expected visibility for the given system and therefore facilitates quantum networks with indistinguishable photons from distributed sources.
We observe a sixfold Purcell broadening of the D_{2} line of an optically trapped ^{87}Rb atom strongly coupled to a fiber cavity. Under external illumination by a near-resonant laser, up to 90% of the atom's fluorescence is emitted into the resonant cavity mode. The sub-Poissonian statistics of the cavity output and the Purcell enhancement of the atomic decay rate are confirmed by the observation of a strongly narrowed antibunching dip in the photon autocorrelation function. The photon leakage through the higher-transmission mirror of the single-sided resonator is the dominant contribution to the field decay (κ≈2π×50 MHz), thus offering a high-bandwidth, fiber-coupled channel for photonic interfaces such as quantum memories and single-photon sources.
We present a novel approach to precisely synthesize arbitrary polarization states of light with a high modulation bandwidth. Our approach consists in superimposing two laser light fields with the same wavelength, but with opposite circular polarizations, where the phase and amplitude of each light field are individually controlled. We find that the polarization-synthesized beam reaches a degree of polarization of 99.99%, which is mainly limited by static spatial variations of the polarization state over the beam profile. We also find that the depolarization caused by temporal fluctuations of the polarization state is about two orders of magnitude smaller. In a recent work, Robens et al. [Phys. Rev. Lett. 118, 065302 (2017)] demonstrated an application of the polarization synthesizer to create two independently controllable optical lattices, which trap atoms depending on their internal spin state. We here use ultracold atoms in polarization-synthesized optical lattices to give an independent, in situ demonstration of the performance of the polarization synthesizer.
High radiation rates are usually associated with macroscopic lasers. Laser radiation is “coherent”—its amplitude and phase are well-defined—but its generation requires energy inputs to overcome loss. Excited atoms spontaneously emit in a random and incoherent fashion, and for N such atoms, the emission rate simply increases as N. However, if these atoms are in close proximity and coherently coupled by a radiation field, this microscopic ensemble acts as a single emitter whose emission rate increases as N2 and becomes “superradiant,” to use Dicke's terminology (1). On page 662 of this issue, Kim et al. (2) show the buildup of coherent light fields through collective emission from atomic radiators injected one by one into a resonator field. There is only one atom ever in the cavity, but the emission is still collective and superradiant. These results suggest another route toward thresholdless lasing.
Recently we have demonstrated scalable, nondestructive, and high-fidelity detection of the internal state of ^{87}Rb neutral atoms in optical dipole traps using state-dependent fluorescence imaging [M. Martinez-Dorantes, W. Alt, J. Gallego, S. Ghosh, L. Ratschbacher, Y. Völzke, and D. Meschede, Phys. Rev. Lett. 119, 180503 (2017)]. In this paper we provide experimental procedures and interpretations to overcome the detrimental effects of heating-induced trap losses and state leakage. We present models for the dynamics of optically trapped atoms during state-dependent fluorescence imaging and verify our results by comparing Monte Carlo simulations with experimental data. Our systematic study of dipole force fluctuations heating in optical traps during near-resonant illumination shows that off-resonant light is preferable for state detection in tightly confining optical potentials.
Quantum statistics have a profound impact on the properties of systems composed of identical particles. At the most elementary level, Bose and Fermi quantum statistics dier in the exchange phase, either 0 or π, which the wavefunction acquires when two identical particles are exchanged. In this Letter, we demonstrate that the exchange phase can be directly probed with a pair of massive particles by physically exchanging their positions. We present two protocols where the particles always remain spatially well separated, thus ensuring that the exchange contribution to their interaction energy is negligible and that the detected signal can only be attributed to the exchange symmetry of the wavefunction. We discuss possible implementations with a pair of trapped atoms or ions.
We demonstrate the parallel and nondestructive readout of the hyperfine state for optically trapped ^{87}Rb atoms. The scheme is based on state-selective fluorescence imaging and achieves detection fidelities > 98% within 10 ms, while keeping 99% of the atoms trapped. For the readout of dense arrays of neutral atoms in optical lattices, where the fluorescence images of neighboring atoms overlap, we apply a novel image analysis technique using Bayesian inference to determine the internal state of multiple atoms. Our method is scalable to large neutral atom registers relevant for future quantum information processing tasks requiring fast and nondestructive readout and can also be used for the simultaneous readout of quantum information stored in internal qubit states and in the atoms’ positions.
We create low-entropy states of neutral atoms by utilizing a conceptually new optical-lattice technique that relies on a high-precision, high-bandwidth synthesis of light polarization. Polarization-synthesized optical lattices provide two fully controllable optical lattice potentials, each of them confining only atoms in either one of the two long-lived hyperfine states. By employing one lattice as the storage register and the other one as the shift register, we provide a proof of concept using four atoms that selected regions of the periodic potential can be filled with one particle per site. We expect that our results can be scaled up to thousands of atoms by employing an atom-sorting algorithm with logarithmic complexity, which is enabled by polarization-synthesized optical lattices. Vibrational entropy is subsequently removed by sideband cooling methods. Our results pave the way for a bottom-up approach to creating ultralow-entropy states of a many-body system.
We have designed, built, and characterized a high- resolution objective lens that is compatible with an ultra-high vacuum environment. The lens system ex- ploits the principle of the Weierstrass-sphere solid immersion lens to reach a numerical aperture (NA) of 0.92. Tailored to the requirements of optical lattice experiments, the objective lens features a relatively long working distance of 150 μm. Our two-lens design is remarkably insensitive to mechanical tolerances in spite of the large NA. Additionally, we demonstrate the application of a tapered optical fiber tip, as used in scanning near-field optical microscopy, to measure the point spread function of a high NA optical system. From the point spread function, we infer the wavefront aberration for the entire field of view of about 75 μm. Pushing the NA of an optical system to its ultimate limit enables novel applications in quantum technolo- gies such as quantum control of atoms in optical mi- crotraps with an unprecedented spatial resolution and photon collection efficiency.
We study the relation between the global topology of the Hofstadter butterfly of a multiband insulator and the topological invariants of the underlying Hamiltonian. The global topology of the butterfly, i.e., the displacement of the energy gaps as the magnetic field is varied by one flux quantum, is determined by the spectral flow of energy eigenstates crossing gaps as the field is tuned. We find that for each gap this spectral flow is equal to the topological invariant of the gap, i.e., the net number of edge modes traversing the gap. For periodically driven systems, our results apply to the spectrum of quasienergies. In this case, the spectral flow of the sum of all the quasienergies gives directly the Rudner-Lindner-Berg-Levin invariant that characterizes the topological phases of a periodically driven system.
We show that the bulk winding number characterizing one-dimensional topological insulators with chiral symmetry can be detected from the displacement of a single particle, observed via losses. Losses represent the effect of repeated weak measurements on one sublattice only, which interrupt the dynamics periodically. When these do not detect the particle, they realize negative measurements. Our repeated measurement scheme covers both time-independent and periodically driven (Floquet) topological insulators, with or without spatial disorder. In the limit of rapidly repeated, vanishingly weak measurements, our scheme describes non-Hermitian Hamiltonians, as the lossy Su-Schrieffer-Heeger model of Rudner and Levitov, [Phys. Rev. Lett. 102, 065703 (2009)]. We find, contrary to intuition, that the time needed to detect the winding number can be made shorter by decreasing the efficiency of the measurement. We illustrate our results on a discrete-time quantum walk, and propose ways of testing them experimentally.
We report on the observation of a topologically protected edge state at the interface between two topologically distinct domains of the Su-Schrieffer-Heeger model, which we implement in arrays of evanescently coupled dielectric-loaded surface plasmon polariton waveguides. Direct evidence of the topological character of the edge state is obtained through several independent experiments: Its spatial localization at the interface as well as the restriction to one sublattice is confirmed by real-space leakage radiation microscopy. The corresponding momentum-resolved spectrum obtained by Fourier imaging reveals the midgap position of the edge state as predicted by theory.
Quanteninformationstechnologien gehören zu den boomenden Forschungsgebieten. Längst geht es nicht mehr allein um Grundlagenforschung, sondern um handfeste technische Anwendungen. Im Fokus ist die abhörsichere Kommunikation. Ein Interview mit Dieter Meschede, Leiter der Arbeitsgruppe Quantentechnologie an der Universität Bonn und künftiger Präsident der Deutschen Physikalischen Gesellschaft.
Discrete-time quantum walks allow Floquet topological insulator materials to be explored using controllable systems such as ultracold atoms in optical lattices. By numerical simulations, we study the robustness of topologically protected edge states in the presence of decoherence in one- and two-dimensional discrete-time quantum walks. We also develop a simple analytical model quantifying the robustness of these edge states against either spin or spatial dephasing, predicting an exponential decay of the population of topologically protected edge states. Moreover, we present an experimental proposal based on neutral atoms in spin-dependent optical lattices to realize spatial boundaries between distinct topological phases. Our proposal relies on a new scheme to implement spin-dependent discrete shift operations in a two-dimensional optical lattice. We analyze under realistic decoherence conditions the experimental feasibility of observing unidirectional, dissipationless transport of matter waves along boundaries separating distinct topological domains.
Fiber Fabry-Perot cavities, formed by micro-machined mirrors on the end-facets of optical fibers, are used in an increasing number of technical and scientific applications, where they typically require precise stabilization of their optical resonances. Here, we study two different approaches to construct fiber Fabry-Perot resonators and stabilize their length for experiments in cavity quantum electrodynamics with neutral atoms. A piezo-mechanically actuated cavity with feedback based on the Pound-Drever-Hall locking technique is compared to a novel rigid cavity design that makes use of the high passive stability of a monolithic cavity spacer and employs thermal self-locking and external temperature tuning. Furthermore, we present a general analysis of the mode matching problem in fiber Fabry-Perot cavities, which explains the asymmetry in their reflective line shapes and has important implications for the optimal alignment of the fiber resonators. Finally, we discuss the issue of fiber-generated background photons. We expect that our results contribute towards the integration of high-finesse fiber Fabry-Perot cavities into compact and robust quantum-enabled devices in the future.
We report on image processing techniques and experimental procedures to determine the lattice-site positions of single atoms in an optical lattice with high reliability, even for limited acquisition time or optical resolution. Determining the positions of atoms beyond the diffraction limit relies on parametric deconvolution in close analogy to methods employed in super-resolution microscopy. We develop a deconvolution method that makes effective use of the prior knowledge of the optical transfer function, noise properties, and discreteness of the optical lattice. We show that accurate knowledge of the image formation process enables a dramatic improvement on the localization reliability. This allows us to demonstrate super-resolution of the atoms' position in closely packed ensembles where the separation between particles cannot be directly optically resolved. Furthermore, we demonstrate experimental methods to precisely reconstruct the point spread function with sub-pixel resolution from fluorescence images of single atoms, and we give a mathematical foundation thereof. We also discuss discretized image sampling in pixel detectors and provide a quantitative model of noise sources in electron multiplying CCD cameras. The techniques developed here are not only beneficial to neutral atom experiments, but could also be employed to improve the localization precision of trapped ions for ultra precise force sensing.
Elitzur and Vaidman have proposed a measurement scheme that, based on the quantum superposition principle, allows one to detect the presence of an object—in a dramatic scenario, a bomb—without interacting with it. It was pointed out by Ghirardi that this interaction-free measurement scheme can be put in direct relation with falsification tests of the macro-realistic worldview. Here we have implemented the "bomb test" with a single atom trapped in a spin-dependent optical lattice to show explicitly a violation of the Leggett-Garg inequality—a quantitative criterion fulfilled by macro-realistic physical theories. To perform interaction-free measurements, we have implemented a novel measurement method that correlates spin and position of the atom. This method, which quantum mechanically entangles spin and position, finds general application for spin measurements, thereby avoiding the shortcomings inherent in the widely used push-out technique. Allowing decoherence to dominate the evolution of our system causes a transition from quantum to classical behavior in fulfillment of the Leggett-Garg inequality.
Even scientific grade optical glasses show birefringence when small external forces are applied to the sample. Stress-induced birefringence can be particularly detrimental to the state of polarization of light when a laser beam is transmitted through the glass. This is especially the case for glass windows of a vacuum chamber. Since compensation of spatially inhomogeneous birefringence is extremely challenging, it should be prevented by proper design of the vacuum chamber. Birefringence below 0.2 nm/cm can be achieved by thoroughly choosing glass material with low stress optical coefficient and mounting geometry. Applications strongly depend on light polarization are quantum technologies such as precision metrology, quantum computation and quantum simulations based on ions or atoms.
We report on a stringent test of the nonclassicality of the motion of a massive quantum particle, which propagates on a discrete lattice. Measuring temporal correlations of the position of single atoms performing a quantum walk, we observe a 6σ violation of the Leggett-Garg inequality. Our results rigorously excludes (i.e., falsifies) any explanation of quantum transport based on classical, well-defined trajectories. We use so-called ideal negative measurements—an essential requisite for any genuine Leggett-Garg test—to acquire information about the atom’s position, yet avoiding any direct interaction with it. The interaction-free measurement is based on a novel atom transport system, which allows us to directly probe the absence rather than the presence of atoms at a chosen lattice site. Beyond the fundamental aspect of this test, we demonstrate the application of the Leggett-Garg correlation function as a witness of quantum superposition. Here, we employ the witness to discriminate different types of walks spanning from merely classical to wholly quantum dynamics.
We report on the observation of cooperative radiation of exactly two neutral atoms strongly coupled to the single mode field of an optical cavity, which is close to the lossless-cavity limit. Monitoring the cavity output power, we observe constructive and destructive interference of collective Rayleigh scattering for certain relative distances between the two atoms. Because of cavity backaction onto the atoms, the cavity output power for the constructive two-atom case (N=2) is almost equal to the single-emitter case (N=1), which is in contrast to free-space where one would expect an N^2 scaling of the power. These effects are quantitatively explained by a classical model as well as by a quantum mechanical model based on Dicke states. We extract information on the relative phases of the light fields at the atom positions and employ advanced cooling to reduce the jump rate between the constructive and destructive atom configurations. Thereby we improve the control over the system to a level where the implementation of two-atom entanglement schemes involving optical cavities becomes realistic.
We report on an ultra-low birefringence dodecagonal glass cell for ultra-high vacuum applications. The epoxy-bonded trapezoidal windows of the cell are made of SF57 glass, which exhibits a very low stress-induced birefringence. We characterize the birefringence Δn of each window with the cell under vacuum conditions, obtaining values around 10^{-8}. After baking the cell at 150 ºC, we reach a pressure below 10^{-10} mbar. In addition, each window is antireflection coated on both sides, which is highly desirable for quantum optics experiments and precision measurements.
Die Erfindung betrifft ein Verfahren, eine Vorrichtung und die Verwendung einer Vorrichtung zur Anwendung oder Messung polarisierter elektromagnetischer Strahlung im Vakuum, wobei die Doppelbrechung Δn < 10^{-6} beträgt.
We report on the state of the art of quantum walk experiments with neutral atoms in state-dependent optical lattices. We demonstrate a novel state-dependent transport technique enabling the control of two spin-selective sublattices in a fully independent fashion. This transport technique allowed us to carry out a test of single-particle quantum interference based on the violation of the Leggett-Garg inequality and, more recently, to probe two-particle quantum interference effects with neutral atoms cooled into the motional ground state. These experiments lay the groundwork for the study of discrete-time quantum walks of strongly interacting, indistinguishable particles to demonstrate quantum cellular automata of neutral atoms.
We demonstrate cooling of the motion of a single neutral atom confined by a dipole trap inside a high-finesse optical resonator. Cooling of the vibrational motion results from electromagnetically induced transparency (EIT)–like interference in an atomic lambda-type configuration, where one transition is strongly coupled to the cavity mode and the other is driven by an external control laser. Good qualitative agreement with the theoretical predictions is found for the explored parameter ranges. Further, we demonstrate EIT cooling of atoms in the dipole trap in free space, reaching the ground state of axial motion. By means of a direct comparison with the cooling inside the resonator, the role of the cavity becomes evident by an additional cooling resonance. These results pave the way towards a controlled interaction among atomic, photonic, and mechanical degrees of freedom.
We analyze the quantum jumps of an atom interacting with a cavity field, where strong coupling makes the cavity transmission depend on the time-dependent atomic state. In our analysis we employ a Bayesian approach that conditions the population of the atomic states at time t on the cavity transmission observed both before and after t, and we show that the state assignment by this approach is more decisive than the usual conditional quantum states based on only earlier measurement data. We also provide an iterative protocol which, together with the atomic state populations, simultaneously estimates the atomic jump rates and the transmission signal distributions from the measurement data. Finally, we take into account technical fluctuations in the observed signal, e.g., due to spatial motion of the atom within the cavity, by representing atomic states by several hidden states, thereby significantly improving the state's recovery.
We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum-walk experiments realized with neutral atoms walking in an optical lattice.
From the measured spatial distributions, we determine with good precision the amount of decoherence per step, which provides a quantitative indication of the quality of our quantum walks. In particular, we find that spin decoherence is the main mechanism responsible for the loss of coherence in our experiment. We also find that the sole observation of ballistic—instead of diffusive—expansion in position space is not a good indicator of the range of coherent delocalization.
We provide further physical insight by distinguishing the effects of short- and long-time spin dephasing mechanisms. We introduce the concept of coherence length in the discrete-time quantum walk, which quantifies the range of spatial coherences. Unexpectedly, we find that quasi-stationary dephasing does not modify the local properties of the quantum walk, but instead affects spatial coherences.
For a visual representation of decoherence phenomena in phase space, we have developed a formalism based on a discrete analogue of the Wigner function. We show that the effects of spin and spatial decoherence differ dramatically in momentum space.
We experimentally realize an enhanced Raman control scheme for neutral atoms that features an intrinsic suppression of the two-photon carrier transition, but retains the sidebands which couple to the external degrees of freedom of the trapped atoms. This is achieved by trapping the atom at the node of a blue detuned standing wave dipole trap, that acts as one field for the two-photon Raman coupling. The improved ratio between cooling and heating processes in this configuration enables a five times lower fundamental temperature limit for resolved sideband cooling. We apply this method to perform Raman cooling to the two-dimensional vibrational ground state and to coherently manipulate the atomic motion. The presented scheme requires minimal additional resources and can be applied to experiments with challenging optical access, as we demonstrate by our implementation for atoms strongly coupled to an optical cavity.
We present an in-situ method to measure the birefringence of a single vacuum window by means of microwave spectroscopy on an ensemble of cold atoms. Stress-induced birefringence can cause an ellipticity in the polarization of an initially linearly-polarized laser beam. The amount of ellipticity can be reconstructed by measuring the differential vector light shift of an atomic hyperfine transition. Measuring the ellipticity as a function of the linear polarization angle allows us to infer the amount of birefringence Δn at the level of 10^{-8} and identify the orientation of the optical axes. The key benefit of this method is the ability to separately characterize each vacuum window, allowing the birefringence to be precisely compensated in existing vacuum apparatuses.
Engineering quantum particle systems, such as quantum simulators and quantum cellular automata, relies on full coherent control of quantum paths at the single particle level. Here we present an atom interferometer operating with single trapped atoms, where single particle wave packets are controlled through spin-dependent potentials. The interferometer is constructed from a sequence of discrete operations based on a set of elementary building blocks, which permit composing arbitrary interferometer geometries in a digital manner. We use this modularity to devise a space-time analogue of the well-known spin echo technique, yielding insight into decoherence mechanisms. We also demonstrate mesoscopic delocalization of single atoms with a separation-to-localization ratio exceeding 500; this result suggests their utilization beyond quantum logic applications as nano-resolution quantum probes in precision measurements, being able to measure potential gradients with precision 5×10^{-4} in units of gravitational acceleration g.
We experimentally demonstrate real-time feedback control of the joint spin-state of two neutral Caesium atoms inside a high finesse optical cavity. The quantum states are discriminated by their different cavity transmission levels. A Bayesian update formalism is used to estimate state occupation probabilities as well as transition rates. We stabilize the balanced two-atom mixed state, which is deterministically inaccessible, via feedback control and find very good agreement with Monte-Carlo simulations. On average, the feedback loops achieves near optimal conditions by steering the system to the target state marginally exceeding the time to retrieve information about its state.
We show that the presence of an interaction in the quantum walk of two atoms leads to the formation of a stable compound, a molecular state. The wave-function of the molecule decays exponentially in the relative position of the two atoms, hence it constitutes a true bound state. Furthermore, for a certain class of interactions we develop an effective theory and find that the dynamics of the molecule is described by a quantum walk in its own right. We propose a setup for the experimental realization as well as sketch the possibility to observe quasi-particle effects in quantum many body systems.
We have directly observed spin-dependent transport of single cesium atoms in a 1D optical lattice. A superposition of two circularly polarized standing waves is generated from two counter propagating, linearly polarized laser beams. Rotation of one of the polarizations by π causes displacement of the σ^{+}- and σ^{–}-lattices by one lattice site. Unidirectional transport over several lattice sites is achieved by rotating the polarization back and forth and flipping the spin after each transport step. We have analyzed the transport efficiency over 10 and more lattice sites, and discussed and quantified relevant error sources.
We experimentally demonstrate the elementary case of electromagnetically induced transparency with a single atom inside an optical cavity probed by a weak field. We observe the modification of the dispersive and absorptive properties of the atom by changing the frequency of a control light field. Moreover, a strong cooling effect has been observed at two-photon resonance, increasing the storage time of our atoms twenty-fold to about 16 seconds. Our result points towards all-optical switching with single photons.
We optically detect the positions of single neutral cesium atoms stored in a standing wave dipole trap with a sub-wavelength resolution of 143 nm rms. The distance between two simultaneously trapped atoms is measured with an even higher precision of 36 nm rms. We resolve the discreteness of the interatomic distances due to the 532 nm spatial period of the standing wave potential and infer the exact number of trapping potential wells separating the atoms. Finally, combining an initial position detection with a controlled transport, we place single atoms at a predetermined position along the trap axis to within 300 nm rms.
We discuss three ways to combine two laser beams with equal linear polarizations and very closely spaced frequencies into a single output beam containing up to 100% of the input power of each beam. One setup, a modified Mach-Zehnder interferometer, is examined in detail; it allows to adjust the combined output power electronically with the help of a simple servo loop. With off-the-shelf optical components we obtained a 98% efficiency.
We have characterized the spectroscopic properties of one of the first samples of blue-emitting diode lasers based on GaN. With such a laser diode operated inside a standard extended cavity arrangement we find a mode-hop free tuning range of more than 20 GHz and a linewidth of 10 MHz. Doppler-free spectroscopy on an indium atomic beam reveals the isotope shift between the two major indium isotopes as well as efficient optical pumping.
Using the stimulated force exerted by counterpropagating π pulses from a mode-locked Ti:sapphire laser we have focused a beam of laser-cooled cesium atoms along one dimension to about 57% of its original width in the detection zone. We determined the force profile outside and inside the overlap region of the pulses and found agreement with an earlier theoretical prediction. The scheme does not require an effective two-level system and is therefore suitable for a large variety of elements.
Grofitechnisch angewandte optische Lithographieverfahrenstofien bei Auflosungen unter 100 nm auf eine prinzipielle Grenze. Die Lithographie mit neutralen Atomstrahlen bietet dazu insbesondere beim parallelen Schreiben periodischer Strukturen eine interessante, noch junge Alternative. Indem man die Wechselwirkung der Atome mit Lichtmasken ausnutzt, gelingt es, grofiflachig periodische Linienmuster und verschiedene zweidimensional periodische Strukturen mit einer Auflosung unter 100 nm zu erzeugen. Dabei werden Atome entweder direkt auf einem Substrat deponiert oder zur Modifikation organischer Resists genutzt. Der folgende Beitrag gibt einen herblick iiber den Stand der Lithographie mit Atomstrahlen.
Threshold photodetachment of negative hydrogen ions stored in a Penning trap has been studied. The electron afﬁnity of hydrogen is determined to 6082.8(7) cm^{−1} in good agreement with previous experiments. The Wigner law has been found to be valid in a region of 400 cm^{−1} above the threshold.
We have fabricated and investigated efficient magnetic lenses, waveguides, and mirrors from rare earth permanent materials. They are affordable and maintenance free. In contrast to corresponding light force components they do not need any supplies, they have large apertures, high reflectivity, and there is no spontaneous emission. The cylindrical shape of magnetic components is furthermore well suited to steer atomic beams.
We have modified a commercial Ti:sapphire laser to allow optical phase stabilization to an extremely stable semiconductor laser, which in turn is locked to a Doppler-free resonance in a cesium vapor cell. For time scales from 10 μs up to several hours the combined system has a rms linewidth of 4 kHz with respect to the cesium resonance. The system allows the resolution of extremely narrow resonances in a cloud of trapped atoms.
With strong rare-earth permanent magnets we have built highly refractive atom-optical components for laser-cooled atoms. We have studied the influence of axially symmetric multipole components on a cesium atomic beam. In analogy to traditional optics the action of a quadrupole ring parallels a conical prism, or axicon. Hexapole lenses were applied for focusing with a more than 1000-fold increase in atomic flux density at the focal spot and for imaging with the atomic beam. Two hexapole lenses were combined to form a telescope, which was operated off axis in order to separate fast thermal and slowed atoms. The experiments can approximately be described in terms of geometrical optics.
We have found that linearly polarized light can be used efficiently for optical trapping of cesium atoms in a magnetic-quadrupole field. The number and density of atoms of the trapped samples are comparable to a standard magneto-optical trap with σ^{+} - σ^{–} polarized light, but the influence of the magnetic-quadrupole strength is strikingly different. When the polarization of counterpropagating light beams is orthogonal, trapping is observed also for zero magnetic field.
The complex magnetic structure of the cesium atom is responsible for the interesting behaviour of its saturated absorption spectra, e.g., a two-fold sign reversal of a crossover resonance, under various polarization configurations with and without applied magnetic fields. We show that this morphology is a result of optical pumping processes including coherent population trapping which, under normal laboratory conditions, prevent the atoms from reaching an equilibrium situation. Our interpretation is useful for an intuitive and rapid understanding of this important tool in high-resolution spectroscopy.
We present the construction of arbitrary multipole field configurations from strong permanent magnets for trapping charged or neutral particles. A general analytic method for the design of three-dimensional magnetic multipoles is discussed for an idealized continuously varying magnetisation taking advantage of the superposition principle. Simple recipes for constructing magnetic dipole and quadrupole fields are given with two types of elements, axially and radially magnetised rings. Cylindrical magnet components not only give free access to the experimental region of interest, but also allow for some tunability to reduce undesirable higher multipole orders. Measurements confirm theoretical predictions achieving useful magnetic fields of 1 T and steep gradients of 3 T/cm with high purity over several ccm.
We discuss an analytic method for the design of three-dimensional magnetic multipoles from permanent magnet materials. The concept is explicited with an idealized, continuously varying magnetization. The effect of segmentation for realistic implementations is discussed. As an example we present an open, experimentally accessible cylindric structure for a dipole and a quadrupole field with high purity. The fields are useful over several cm^{3}.