Universal Dynamics of Rogue Waves in a Quenched Spinor Bose Condensate

Isolated many-body systems far from equilibrium may exhibit scaling dynamics with universal exponents indicating the proximity of the time evolution to a nonthermal fixed point. We find universal dynamics connected with the occurrence of extreme wave excitations in the mutually coupled magnetic components of a spinor gas which propagate in an effectively random potential. The frequency of these rogue waves is affected by the time-varying spatial correlation length of the potential, giving rise to an additional exponent δ_{c}≃1/3 for temporal scaling, which is different from the exponent β_{V}≃1/4 characterizing the scaling of the correlation length ℓ_{V}∼t^{β_{V}} in time. As a result of the caustics, i.e., focusing events, real-time instanton defects appear in the Larmor phase of the spin-1 system as vortices in space and time. The temporal correlations governing the instanton occurrence frequency scale as t^{δ_{I}}. This suggests that the universality class of a nonthermal fixed point could be characterized by different, mutually related exponents defining the evolution in time and space, respectively. Our results have a strong relevance for understanding pattern coarsening from first principles and potential implications for dynamics ranging from the early Universe to geophysical dynamics and microphysics.

Quantum field simulator for dynamics in curved spacetime

In most cosmological models, rapid expansion of space marks the first moments of the Universe and leads to the amplification of quantum fluctuations¹. The description of subsequent dynamics and related questions in cosmology requires an understanding of the quantum fields of the standard model and dark matter in curved spacetime. Even the reduced problem of a scalar quantum field in an explicitly time-dependent spacetime metric is a theoretical challenge^2-5, and thus a quantum field simulator can lead to insights. Here we demonstrate such a quantum field simulator in a two-dimensional Bose-Einstein condensate with a configurable trap^6,7 and adjustable interaction strength to implement this model system. We explicitly show the realization of spacetimes with positive and negative spatial curvature by wave-packet propagation and observe particle-pair production in controlled power-law expansion of space, using Sakharov oscillations to extract amplitude and phase information of the produced state. We find quantitative agreement with analytical predictions for different curvatures in time and space. This benchmarks and thereby establishes a quantum field simulator of a new class. In the future, straightforward upgrades offer the possibility to enter unexplored regimes that give further insight into relativistic quantum field dynamics.

Detecting Entanglement Structure in Continuous Many-Body Quantum Systems

A prerequisite for the comprehensive understanding of many-body quantum systems is a characterization in terms of their entanglement structure. The experimental detection of entanglement in spatially extended many-body systems describable by quantum fields still presents a major challenge. We develop a general scheme for certifying entanglement and demonstrate it by revealing entanglement between distinct subsystems of a spinor Bose-Einstein condensate. Our scheme builds on the spatially resolved simultaneous detection of the quantum field in two conjugate observables which allows the experimental confirmation of quantum correlations between local as well as nonlocal partitions of the system. The detection of squeezing in Bogoliubov modes in a multimode setting illustrates its potential to boost the capabilities of quantum simulations to study entanglement in spatially extended many-body systems.

High signal to noise absorption imaging of alkali atoms at moderate magnetic fields

We present an improved scheme for absorption imaging of alkali atoms at moderate magnetic fields, where the excited state is well in the Paschen-Back regime, but the ground state hyperfine manifold is not. It utilizes four atomic levels to obtain an approximately closed optical cycle. With the resulting absorption of the corresponding two laser frequencies, we extract the atomic column density of a ³⁹K Bose-Einstein condensate. The scheme can be readily applied to all other alkali-like species.

Collisions of Three-Component Vector Solitons in Bose-Einstein Condensates

Ultracold gases provide an unprecedented level of control for the investigation of soliton dynamics and collisions. We present a scheme for deterministically preparing pairs of three-component solitons in a Bose-Einstein condensate. Our method is based on local spin rotations which simultaneously imprint suitable phase and density distributions. This enables us to observe striking collisional properties of the vector degree of freedom which naturally arises for the coherent nature of the emerging multicomponent solitons. We find that the solitonic properties in the quasi-one-dimensional system are quantitatively described by the integrable repulsive three-component Manakov model.

A scalable realization of local U(1) gauge invariance in cold atomic mixtures

In the fundamental laws of physics, gauge fields mediate the interaction between charged particles. An example is the quantum theory of electrons interacting with the electromagnetic field, based on U(1) gauge symmetry. Solving such gauge theories is in general a hard problem for classical computational techniques. Although quantum computers suggest a way forward, large-scale digital quantum devices for complex simulations are difficult to build. We propose a scalable analog quantum simulator of a U(1) gauge theory in one spatial dimension. Using interspecies spin-changing collisions in an atomic mixture, we achieve gauge-invariant interactions between matter and gauge fields with spin- and species-independent trapping potentials. We experimentally realize the elementary building block as a key step toward a platform for quantum simulations of continuous gauge theories.

Simultaneous Readout of Noncommuting Collective Spin Observables beyond the Standard Quantum Limit

We augment the information extractable from a single absorption image of a spinor Bose-Einstein condensate by coupling to initially empty auxiliary hyperfine states. Performing unitary transformations in both the original and auxiliary hyperfine manifold enables the simultaneous measurement of multiple spin-1 observables. We apply this scheme to an elongated atomic cloud of ^{87}Rb to simultaneously read out three orthogonal spin directions and with that directly access the spatial spin structure. The readout even allows the extraction of quantum correlations which we demonstrate by detecting spin-nematic squeezing without state tomography.

Spatially distributed multipartite entanglement enables EPR steering of atomic clouds

A key resource for distributed quantum-enhanced protocols is entanglement between spatially separated modes. However, the robust generation and detection of entanglement between spatially separated regions of an ultracold atomic system remain a challenge. We used spin mixing in a tightly confined Bose-Einstein condensate to generate an entangled state of indistinguishable particles in a single spatial mode. We show experimentally that this entanglement can be spatially distributed by self-similar expansion of the atomic cloud. We used spatially resolved spin read-out to reveal a particularly strong form of quantum correlations known as Einstein-Podolsky-Rosen (EPR) steering between distinct parts of the expanded cloud. Based on the strength of EPR steering, we constructed a witness, which confirmed genuine 5-partite entanglement.

Universal equilibrium scaling functions at short times after a quench

By analyzing spin-spin correlation functions at relatively short distances, we show that equilibrium near-critical properties can be extracted at short times after quenches into the vicinity of a quantum critical point. The time scales after which equilibrium properties can be extracted are sufficiently short so that the proposed scheme should be viable for quantum simulators of spin models based on ultracold atoms or trapped ions. Our results, analytic as well as numeric, are for one-dimensional spin models, either integrable or nonintegrable, but we expect our conclusions to be valid in higher dimensions as well.

Dissipative Double-Well Potential for Cold Atoms: Kramers Rate and Stochastic Resonance

We experimentally study particle exchange in a dissipative double-well potential using laser-cooled atoms in a hybrid trap. We measure the particle hopping rate as a function of barrier height, temperature, and atom number. Single-particle resolution allows us to measure rates over more than 4 orders of magnitude and distinguish the effects of loss and hopping. Deviations from the Arrhenius-law scaling at high barrier heights occur due to cold collisions between atoms within a well. By driving the system periodically, we characterize the phenomenon of stochastic resonance in the system response.

Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics

We experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies.

Observation of Scaling in the Dynamics of a Strongly Quenched Quantum Gas

We report on the experimental observation of scaling in the time evolution following a sudden quench into the vicinity of a quantum critical point. The experimental system, a two-component Bose gas with coherent exchange between the constituents, allows for the necessary high level of control of parameters as well as the access to time-resolved spatial correlation functions. The theoretical analysis reveals that when quenching the system close to the critical point, the energy introduced by the quench leads to a short-time evolution exhibiting crossover reminiscent of the finite-temperature critical properties in the system's universality class. Observing the time evolution after a quench represents a paradigm shift in accessing and probing experimentally universal properties close to a quantum critical point and allows in a new way benchmarking of quantum many-body theory with experiments.

Scalable spin squeezing for quantum-enhanced magnetometry with Bose-Einstein condensates

A major challenge in quantum metrology is the generation of entangled states with a macroscopic atom number. Here, we demonstrate experimentally that atomic squeezing generated via nonlinear dynamics in Bose-Einstein condensates, combined with suitable trap geometries, allows scaling to large ensemble sizes. We achieve a suppression of fluctuations by 5.3(5) dB for 12,300 particles, from which we infer that similar squeezing can be obtained for more than 10(7)  atoms. With this resource, we demonstrate quantum-enhanced magnetometry by swapping the squeezed state to magnetically sensitive hyperfine levels that have negligible nonlinearity. We find a quantum-enhanced single-shot sensitivity of 310(47) pT for static magnetic fields in a probe volume as small as 90  μm3.

Accurate atom counting in mesoscopic ensembles

Many cold atom experiments rely on precise atom number detection, especially in the context of quantum-enhanced metrology where effects at the single particle level are important. Here, we investigate the limits of atom number counting via resonant fluorescence detection for mesoscopic samples of trapped atoms. We characterize the precision of these fluorescence measurements beginning from the single-atom level up to more than one thousand. By investigating the primary noise sources, we obtain single-atom resolution for atom numbers as high as 1200. This capability is an essential prerequisite for future experiments with highly entangled states of mesoscopic atomic ensembles.

Motional coherence of fermions immersed in a Bose gas

We prepare a superposition of two motional states by addressing lithium atoms immersed in a Bose-Einstein condensate of sodium with a species-selective potential. The evolution of the superposition state is characterized by the populations of the constituent states as well as their coherence. The latter we extract employing a novel scheme analogous to the spin-echo technique. Comparing the results directly to measurements on freely evolving fermions allows us to isolate the decoherence effects induced by the bath. In our system, the decoherence time is close to the maximal possible value since the decoherence is dominated by population relaxation processes. The measured data are in good agreement with a theoretical model based on Fermi's golden rule.

Rabi flopping induces spatial demixing dynamics

We experimentally investigate the mixing and demixing dynamics of Bose-Einstein condensates in the presence of a linear coupling between two internal states. The observed amplitude reduction of the Rabi oscillations can be understood as a result of demixing dynamics of dressed states as experimentally confirmed by reconstructing the spatial profile of dressed state amplitudes. The observations are in quantitative agreement with numerical integration of coupled Gross-Pitaevskii equations without free parameters, which also reveals the criticality of the dynamics on the symmetry of the system. Our observations demonstrate new possibilities for changing effective atomic interactions and studying critical phenomena.

Classical bifurcation at the transition from Rabi to Josephson dynamics

We report on the experimental demonstration of the internal bosonic Josephson effect in a rubidium spinor Bose-Einstein condensate. The measurement of the full time dynamics in phase space allows the characterization of the theoretically predicted π-phase modes and quantitatively confirms analytical predictions, revealing a classical bifurcation. Our results suggest that this system is a model system which can be tuned from classical to the quantum regime and thus is an important step towards the experimental investigation of entanglement generation close to critical points.

Hyperfine spectroscopy of the 1s(5)-2p(9) transition of 39Ar

We report on the first experimental determination of the hyperfine structure of the 1s(5)-2p(9) transition in (39)Ar. We give a detailed description of the sample preparation, spectroscopy cell cleaning, and spectroscopic setup. The resulting set of parameters consists of the hyperfine constants of the levels involved and the isotopic shift between (39)Ar and (40)Ar. With the achieved precision all laser frequencies necessary for the implementation of atom trap trace analysis for (39)Ar, i.e., laser cooling and repumping frequencies, are now known.

Experimental observation of oscillating and interacting matter wave dark solitons

We report on the generation, subsequent oscillation and interaction of a pair of matter-wave dark solitons. These are created by releasing a Bose-Einstein condensate from a double well potential into a harmonic trap in the crossover regime between one dimension and three dimensions. Multiple oscillations and collisions of the solitons are observed, in quantitative agreement with simulations of the Gross-Pitaevskii equation. An effective particle picture is developed and confirms that the deviation of the observed oscillation frequencies from the asymptotic prediction nu(z)/sqrt 2, where nu(z) is the longitudinal trapping frequency, results from the dimensionality of the system and the soliton interactions.

Single-particle tunneling in strongly driven double-well potentials

We report on the first direct observation of coherent control of single-particle tunneling in a strongly driven double-well potential. In our setup atoms propagate in a periodic arrangement of double wells allowing the full control of the driving parameters such as frequency, amplitude, and even the space-time symmetry. Our experimental findings are in quantitative agreement with the predictions of the corresponding Floquet theory and are also compared to the predictions of a simple two mode model. Our experiments reveal directly the critical dependence of coherent destruction of tunneling on the generalized parity symmetry.

Noise thermometry with two weakly coupled Bose-Einstein condensates

Here we report on the experimental investigation of thermally induced fluctuations of the relative phase between two Bose-Einstein condensates which are coupled via tunneling. The experimental control over the coupling strength and the temperature of the thermal background allows for the quantitative analysis of the phase fluctuations. Furthermore, we demonstrate the application of these measurements for thermometry in a regime where standard methods fail. With this we confirm that the heat capacity of an ideal Bose gas deviates from that of a classical gas as predicted by the third law of thermodynamics.

Observation of nonspreading wave packets in an imaginary potential

We propose and experimentally demonstrate a method to prepare a nonspreading atomic wave packet. Our technique relies on a spatially modulated absorption constantly chiseling away from an initially broad de Broglie wave. The resulting contraction is balanced by dispersion due to Heisenberg's uncertainty principle. This quantum evolution results in the formation of a nonspreading wave packet of Gaussian form with a spatially quadratic phase. Experimentally, we confirm these predictions by observing the evolution of the momentum distribution. Moreover, by employing interferometric techniques, we measure the predicted quadratic phase across the wave packet. Nonspreading wave packets of this kind also exist in two space dimensions and we can control their amplitude and phase using optical elements.

Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction

We report on the first realization of a single bosonic Josephson junction, implemented by two weakly linked Bose-Einstein condensates in a double-well potential. In order to fully investigate the nonlinear tunneling dynamics we measure the density distribution in situ and deduce the evolution of the relative phase between the two condensates from interference fringes. Our results verify the predicted nonlinear generalization of tunneling oscillations in superconducting and superfluid Josephson junctions. Additionally, we confirm a novel nonlinear effect known as macroscopic quantum self-trapping, which leads to the inhibition of large amplitude tunneling oscillations.

Nonlinear self-trapping of matter waves in periodic potentials

We report the first experimental observation of nonlinear self-trapping of Bose-condensed 87Rb atoms in a one-dimensional waveguide with a superimposed deep periodic potential . The trapping effect is confirmed directly by imaging the atomic spatial distribution. Increasing the nonlinearity we move the system from the diffusive regime, characterized by an expansion of the condensate, to the nonlinearity dominated self-trapping regime, where the initial expansion stops and the width remains finite. The data are in quantitative agreement with the solutions of the corresponding discrete nonlinear equation. Our results reveal that the effect of nonlinear self-trapping is of local nature, and is closely related to the macroscopic self-trapping phenomenon already predicted for double-well systems.

Quantum features in atomic nanofabrication using exactly resonant standing waves

We report on the first fabrication of nanostructures with exactly resonant light revealing the quantum character of the atom-light interaction. Classically the formation of nanostructures is not expected; thus, the observed formation of complex periodic line patterns can be explained only by treating atom-light interaction and propagation of the atoms quantum mechanically. Our numerical quantum calculations are in quantitative agreement with this experimental finding. Moreover, the theory predicts that for small detunings nanostructures with lambda/4 period can be produced, which beats the standard nanofabrication limit of lambda/2. Our experiments confirm this prediction.

Bright Bose-Einstein gap solitons of atoms with repulsive interaction

We report on the first experimental observation of bright matter wave solitons for 87Rb atoms with repulsive atom-atom interaction. This counterintuitive situation arises inside a weak periodic potential, where anomalous dispersion can be realized at the Brillouin zone boundary. If the coherent atomic wave packet is prepared at the corresponding band edge, a bright soliton is formed inside the gap. The strength of our system is the precise control of preparation and real time manipulation, allowing the systematic investigation of gap solitons.

Dispersion management for atomic matter waves

We demonstrate the control of the dispersion of matter wave packets utilizing periodic potentials. This is analogous to the technique of dispersion management known in photon optics. Matter wave packets are realized by Bose-Einstein condensates of 87Rb in an optical dipole potential acting as a one-dimensional waveguide. A weak optical lattice is used to control the dispersion relation of the matter waves during the propagation of the wave packets. The dynamics are observed in position space and interpreted using the concept of effective mass. By switching from positive to negative effective mass, the dynamics can be reversed. The breakdown of the approximation of constant, as well as experimental signatures of an infinite effective mass are studied.

Approaching classicality in quantum accelerator modes through decoherence

We describe measurements of the mean energy of an ensemble of laser-cooled atoms in an atom optical system in which the cold atoms, falling freely under gravity, receive approximate delta-kicks from a pulsed standing wave of laser light. We call this system a "delta-kicked accelerator." Additionally, we can counteract the effect of gravity by appropriate shifting of the position of the standing wave, which restores the dynamics of the standard delta-kicked rotor. The presence of gravity (delta-kicked accelerator) yields quantum phenomena, quantum accelerator modes, which are markedly different from those in the case for which gravity is absent (delta-kicked rotor). Quantum accelerator modes result in a much higher rate of increase in the mean energy of the system than is found in its classical analog. When gravity is counteracted, the system exhibits the suppression of the momentum diffusion characteristic of dynamical localization. The effect of noise is examined and a comparison is made with simulations of both quantum-mechanical and classical versions of the system. We find that the introduction of noise results in the restoration of several signatures of classical behavior, although significant quantum features remain.

Quantum enhancement of momentum diffusion in the delta-kicked rotor

We present detailed observations of the quantum delta-kicked rotor in the vicinity of a quantum resonance. Our experiment consists of an ensemble of cold cesium atoms subject to a pulsed off-resonant standing wave of light. We measure the mean energy and show clearly that at the quantum resonance it is a local maximum. We also examine the effect of noise on the system and find that the greatest sensitivity to this occurs at the resonances. This makes these regions ideal for examining quantum-classical correspondence. A picture based on diffraction is developed which allows the experiments to be readily understood.