Generation of macroscopic pair-correlated atomic beams by four-wave mixing in Bose-Einstein condensates

Spin- and Momentum-Correlated Atom Pairs Mediated by Photon Exchange and Seeded by Vacuum Fluctuations

Engineering pairs of massive particles that are simultaneously correlated in their external and internal degrees of freedom is a major challenge, yet essential for advancing fundamental tests of physics and quantum technologies. In this Letter, we experimentally demonstrate a mechanism for generating pairs of atoms in well-defined spin and momentum modes. This mechanism couples atoms from a degenerate Bose gas via a superradiant photon-exchange process in an optical cavity, producing pairs via a single channel or two discernible channels. The scheme is independent of collisional interactions, fast, and tunable. We observe a collectively enhanced production of pairs and probe interspin correlations in momentum space. We characterize the emergent pair statistics and find that the observed dynamics is consistent with being primarily seeded by vacuum fluctuations in the corresponding atomic modes. Together with our observations of coherent many-body oscillations involving well-defined momentum modes, our results offer promising prospects for quantum-enhanced interferometry and quantum simulation experiments using entangled matter waves.

Generating Multiparticle Entangled States by Self-Organization of Driven Ultracold Atoms

We describe a mechanism for guiding the dynamical evolution of ultracold atomic motional degrees of freedom toward multiparticle entangled Dicke-squeezed states, via nonlinear self-organization under external driving. Two examples of many-body models are investigated. In the first model, the external drive is a temporally oscillating magnetic field leading to self-organization by interatomic scattering. In the second model, the drive is a pump laser leading to transverse self-organization by photon-atom scattering in a ring cavity. We numerically demonstrate the generation of multiparticle entangled states of atomic motion and discuss prospective experimental realizations of the models. For the cavity case, the calculations with adiabatically eliminated photonic sidebands show significant momentum entanglement generation can occur even in the "bad cavity" regime. The results highlight the potential for using self-organization of atomic motion in quantum technological applications.

On the survival of the quantum depletion of a condensate after release from a magnetic trap

We present observations of the high momentum tail in expanding Bose-Einstein condensates of metastable Helium atoms released from a harmonic trap. The far-field density profile exhibits features that support identification of the tails of the momentum distribution as originating in the in-situ quantum depletion prior to release. Thus, we corroborate recent observations of slowly-decaying tails in the far-field beyond the thermal component. This observation is in conflict with the hydrodynamic theory, which predicts that the in-situ depletion does not survive when atoms are released from a trap. Indeed, the depleted tails even appear stronger in the far-field than expected before release, and we discuss the challenges of interpreting this in terms of the Tan contact in the trapped gas. In complement to these observations, full quantum simulations of the experiment show that, under the right conditions, the depletion can persist into the far field after expansion. Moreover, the simulations provide mechanisms for survival and for the the large-momentum tails to appear stronger after expansion due to an acceleration of the depleted atoms by the mean-field potential. However, while in qualitative agreement, the final depletion observed in the experiment is much larger than in the simulation.

Emission of Spin-Correlated Matter-Wave Jets from Spinor Bose-Einstein Condensates

We report the observation of matter-wave jet emission in a strongly ferromagnetic spinor Bose-Einstein condensate of ^{7}Li atoms. Directional atomic beams with |F=1,m_{F}=1⟩ and |F=1,m_{F}=-1⟩ spin states are generated from |F=1,m_{F}=0⟩ state condensates or vice versa. This results from collective spin-mixing scattering events, where spontaneously produced pairs of atoms with opposite momentum facilitates additional spin-mixing collisions as they pass through the condensates. The matter-wave jets of different spin states (|F=1,m_{F}=±1⟩) can be a macroscopic Einstein-Podolsky-Rosen state with spacelike separation. Its spin-momentum correlations are studied by using the angular correlation function for each spin state. Rotating the spin axis, the inter- and intraspin-momentum correlation peaks display a high-contrast oscillation, indicating collective coherence of the atomic ensembles. We provide numerical calculations that describe the experimental results at a quantitative level. Our Letter paves the way to generating macroscopic quantum entanglement with the spin and motional degree of freedom with massive particles. It has a wide range of applications from quantum information science to the fundamental studies of quantum entanglement.

Spin distillation cooling of ultracold Bose gases

We study the spin distillation of spinor gases of bosonic atoms and find two different mechanisms in [Formula: see text]Cr and [Formula: see text]Na atoms, both of which can cool effectively. The first mechanism involves dipolar scattering into initially unoccupied spin states and cools only above a threshold magnetic field. The second proceeds via equilibrium relaxation of the thermal cloud into empty spin states, reducing its proportion in the initial component. It cools only below a threshold magnetic field. The technique was initially demonstrated experimentally for a chromium dipolar gas (Naylor et al. in Phys Rev Lett 115:243002, 2015), whereas here we develop the concept further and provide an in-depth understanding of the required physics and limitations involved. Through numerical simulations, we reveal the mechanisms involved and demonstrate that the spin distillation cycle can be repeated several times, each time resulting in a significant additional reduction of the thermal atom fraction. Threshold values of magnetic field and predictions for the achievable temperature are also identified.

Gain through losses in nonlinear optics

Instabilities of uniform states are ubiquitous processes occurring in a variety of spatially extended nonlinear systems. These instabilities are at the heart of symmetry breaking, condensate dynamics, self-organisation, pattern formation, and noise amplification across diverse disciplines, including physics, chemistry, engineering, and biology. In nonlinear optics, modulation instabilities are generally linked to the so-called parametric amplification process, which occurs when certain phase-matching or quasi-phase-matching conditions are satisfied. In the present review article, we summarise the principle results on modulation instabilities and parametric amplification in nonlinear optics, with special emphasis on optical fibres. We then review state-of-the-art research about a peculiar class of modulation instabilities (MIs) and signal amplification processes induced by dissipation in nonlinear optical systems. Losses applied to certain parts of the spectrum counterintuitively lead to the exponential growth of the damped mode themselves, causing gain through losses. We discuss the concept of imaging of losses into gain, showing how to map a given spectral loss profile into a gain spectrum. We demonstrate with concrete examples that dissipation-induced MI, apart from being of fundamental theoretical interest, may pave the way towards the design of a new class of tuneable fibre-based optical amplifiers, optical parametric oscillators, frequency comb sources, and pulsed lasers.

A unified ab initio approach to the correlated quantum dynamics of ultracold fermionic and bosonic mixtures

We extent the recently developed Multi-Layer Multi-Configuration Time-Dependent Hartree method for Bosons for simulating the correlated quantum dynamics of bosonic mixtures to the fermionic sector and establish a unifying approach for the investigation of the correlated quantum dynamics of a mixture of indistinguishable particles, be it fermions or bosons. Relying on a multi-layer wave-function expansion, the resulting Multi-Layer Multi-Configuration Time-Dependent Hartree method for Mixtures (ML-MCTDHX) can be adapted to efficiently resolve system-specific intra- and inter-species correlations. The versatility and efficiency of ML-MCTDHX are demonstrated by applying it to the problem of colliding few-atom mixtures of both Bose-Fermi and Fermi-Fermi types. Thereby, we elucidate the role of correlations in the transmission and reflection properties of the collisional events. In particular, we present examples where the reflection (transmission) at the other atomic species is a correlation-dominated effect, i.e., it is suppressed in the mean-field approximation.

Bell Inequality, Einstein-Podolsky-Rosen Steering, and Quantum Metrology with Spinor Bose-Einstein Condensates

We propose an experiment, where the Bell inequality is violated in a many-body system of massive particles. The source of correlated atoms is a spinor F=1 Bose-Einstein condensate residing in an optical lattice. We characterize the complete procedure-the local operations, the measurements, and the inequality-necessary to run the Bell test. We show how the degree of violation of the Bell inequality depends on the strengths of the two-body correlations and on the number of scattered pairs. We show that the system can be used to demonstrate the Einstein-Podolsky-Rosen paradox. Also, the scattered pairs are an excellent many-body resource for the quantum-enhanced metrology. Our results apply to any multimode system where the spin-changing collision drives the scattering into separate regions. The presented inquiry shows that such a system is versatile as it can be used for the tests of nonlocality, quantum metrology, and quantum information.

Dissociation of One-Dimensional Matter-Wave Breathers due to Quantum Many-Body Effects

We use the ab initio Bethe ansatz dynamics to predict the dissociation of one-dimensional cold-atom breathers that are created by a quench from a fundamental soliton. We find that the dissociation is a robust quantum many-body effect, while in the mean-field (MF) limit the dissociation is forbidden by the integrability of the underlying nonlinear Schrödinger equation. The analysis demonstrates the possibility to observe quantum many-body effects without leaving the MF range of experimental parameters. We find that the dissociation time is of the order of a few seconds for a typical atomic-soliton setting.

Squeezing and Entanglement of Density Oscillations in a Bose-Einstein Condensate

The dispersive interaction of atoms and a far-detuned light field allows nondestructive imaging of the density oscillations in Bose-Einstein condensates. Starting from a ground state condensate, we investigate how the measurement backaction leads to squeezing and entanglement of the quantized density oscillations. We show that properly timed, stroboscopic imaging and feedback can be used to selectively address specific eigenmodes and avoid excitation of nontargeted modes of the system.

Strong quantum spin correlations observed in atomic spin mixing

We have observed sub-Poissonian spin correlations generated by collisionally induced spin mixing in a spin-1 Bose-Einstein condensate. We measure a quantum noise reduction of -7 dB (-10 dB corrected for detection noise) below the standard quantum limit for the corresponding coherent spin states. The spin fluctuations are detected as atom number differences in the spin states using fluorescent imaging that achieves a detection noise floor of 8 atoms per spin component for a probe time of 100 μs.

Correlations in amplified four-wave mixing of matter waves

The coherence properties of amplified matter waves generated by four-wave mixing (FWM) are studied using the Hanbury-Brown-Twiss method. We examine two limits. In the first case stimulated processes lead to the selective excitation of a pair of spatially separated modes, which we show to be second order coherent, while the second occurs when the FWM process is multimode, due to spontaneous scattering events which leads to incoherent matter waves. Amplified FWM is a promising candidate for fundamental tests of quantum mechanics where correlated modes with large occupations are required.

Collinear four-wave mixing of two-component matter waves

We demonstrate atomic four-wave mixing of two-component matter waves in a collinear geometry. Starting from a single-species Bose-Einstein condensate, seed and pump modes are prepared through microwave state transfer and state-selective Kapitza-Dirac diffraction. Four-wave mixing then populates the initially empty output modes. Simulations based on a coupled-mode expansion of the Gross-Pitaevskii equation are in very good agreement with the experimental data. We show that four-wave mixing can play an important role in studies of bosonic mixtures in optical lattices. Moreover, our system should be of interest in the context of quantum atom optics.

Spontaneous four-wave mixing of de Broglie waves: beyond optics

We investigate the atom-optical analog of degenerate four-wave mixing by colliding two Bose-Einstein condensates of metastable helium. The momentum distribution of the scattered atoms is measured in three dimensions. A simple analogy with photon phase matching conditions suggests a spherical final distribution. We find, however, that it is an ellipsoid with radii smaller than the initial collision momenta. Numerical and analytical calculations agree with this and reveal the interplay between many-body effects, mean-field interaction, and the anisotropy of the source condensate.

Simulation of complete many-body quantum dynamics using controlled quantum-semiclassical hybrids

A controlled hybridization between full quantum dynamics and semiclassical approaches (mean-field and truncated Wigner) is implemented for interacting many-boson systems. It is then demonstrated how simulating the resulting hybrid evolution equations allows one to obtain the full quantum dynamics for much longer times than is possible using an exact treatment directly. A collision of sodium BECs with 1.5 x 10;{5} atoms is simulated, in a regime that is difficult to describe semiclassically. The uncertainty of physical quantities depends on the statistics of the full quantum prediction. Cutoffs are minimized to a discretization of the Hamiltonian. The technique presented is quite general and extension to other systems is considered.

Observation of atom pairs in spontaneous four-wave mixing of two colliding Bose-Einstein condensates

We study atom scattering from two colliding Bose-Einstein condensates using a position sensitive, time resolved, single atom detector. In analogy to quantum optics, the process can also be thought of as spontaneous, degenerate four-wave mixing of de Broglie waves. We find a clear correlation between atoms with opposite momenta, demonstrating pair production in the scattering process. We also observe a Hanbury Brown-Twiss correlation for collinear momenta, which permits an independent measurement of the size of the pair production source and thus the size of the spatial mode. The back-to-back pairs occupy very nearly two oppositely directed spatial modes, a promising feature for future quantum optics experiments.

Correlations in a BEC collision: first-principles quantum dynamics with 150,000 atoms

The quantum dynamics of colliding Bose-Einstein condensates with 150,000 atoms are simulated directly from the Hamiltonian using the stochastic positive-P method. Two-body correlations between the scattered atoms and their velocity distribution are found for experimentally accessible parameters. Hanbury Brown-Twiss or thermal-like correlations are seen for copropagating atoms, while number correlations for counterpropagating atoms are even stronger than thermal correlations at short times. The coherent phase grains grow in size as the collision progresses with the onset of growth coinciding with the beginning of stimulated scattering. The method is versatile and usable for a range of cold atom systems.

Simulation of a single collision of two bose-einstein condensates

We propose a method for simulating a single realization of a collision of two Bose-Einstein condensates. Recently [Phys. Rev. Lett. 94, 200401 (2005)], we introduced a quantum model of incoherent elastic scattering in a collision of two counterpropagating atomic Gaussian wave packets. Here we show that this model is capable of generating data that can be interpreted as results of a single collisional event. We find a range of parameters, including relative velocity, population, and the size of colliding condensates, where the structure of the halo of scattered atoms in a single realization strongly differs from that averaged over many realizations.

Bose-Einstein condensation with an entangled order parameter

We propose a practically accessible non-mean-field ground state of Bose-Einstein condensation, which occurs in an interspecies two-particle entangled state, and is thus described by an entangled order parameter. A suitably defined entanglement entropy is used as the characterization of the non-mean-field nature, and is found to persist in a wide parameter regime. The interspecies entanglement leads to novel interference terms in the dynamical equations governing the single-particle orbital wave function. Experimental feasibility and several methods of probe are discussed. We urge the study of multichannel scattering between different species of atoms.

Parametric amplification of scattered atom pairs

We have observed parametric generation and amplification of ultracold atom pairs. A 87Rb Bose-Einstein condensate was loaded into a one-dimensional optical lattice with quasimomentum k0 and spontaneously scattered into two final states with quasimomenta k1 and k2 . Furthermore, when a seed of atoms was first created with quasimomentum k1 we observed parametric amplification of scattered atoms pairs in states k1 and k2 when the phase-matching condition was fulfilled. This process is analogous to optical parametric generation and amplification of photons and could be used to efficiently create entangled pairs of atoms. Furthermore, these results explain the dynamic instability of condensates in moving lattices observed in recent experiments.

Hanbury Brown Twiss Effect for Ultracold Quantum Gases

We have studied two-body correlations of atoms in an expanding cloud above and below the Bose-Einstein condensation threshold. The observed correlation function for a thermal cloud shows a bunching behavior, whereas the correlation is flat for a coherent sample. These quantum correlations are the atomic analog of the Hanbury Brown Twiss effect. We observed the effect in three dimensions and studied its dependence on cloud size.

Parametric amplification of matter waves in periodically translated optical lattices

We observe the sudden growth of small classes of Bloch waves from atomic Bose-Einstein condensates held in periodically translated optical lattices. The effect is explained by narrowband parametric amplification of Bloch waves from noise, due to phase-matched scattering of atom pairs out of the condensate. Amplification occurs above a well-defined modulation threshold, described by dynamic shaping of single-particle band structure.

Quantum multimode model of elastic scattering from Bose-Einstein condensates

Mean field approximation treats only coherent aspects of the evolution of a Bose-Einstein condensate. However, in many experiments some atoms scatter out of the condensate. We study a semianalytic model of two counterpropagating atomic Gaussian wave packets incorporating the dynamics of incoherent scattering processes. Within the model we can treat processes of the elastic collision of atoms into the initially empty modes, and observe how, with growing occupation, the bosonic enhancement is slowly kicking in. A condition for the bosonic enhancement effect is found in terms of relevant parameters. Scattered atoms form a squeezed state. Not only are we able to calculate the dynamics of mode occupation, but also the full statistics of scattered atoms.

Quantum turbulence in condensate collisions: an application of the classical field method

We apply the classical field method to simulate the production of correlated atoms during the collision of two Bose-Einstein condensates. Our nonperturbative method includes the effect of quantum noise, and describes collisions of high density condensates with very large out-scattered fractions. Quantum correlation functions for the scattered atoms show that the correlation between pairs of atoms of opposite momentum is rather small. We also predict the existence of quantum turbulence in the field of the scattered atoms.

Fully quantized theory of four-wave mixing with bosonic matter waves

We solve exactly a set of fully quantized coupled equations that describe the quantum dynamics, including the evolution of quantum fluctuations, entanglements, and correlations, of four-wave mixing (FWM) with matter waves. The analytical solution reveals Rabi oscillations, collapses and revivals, and agrees with FWM experiments. It also applies to optical FWM and the Rayleigh superradiance in Bose-Einstein condensates.

Interferometric determination of the s and d-wave scattering amplitudes in 87Rb

We demonstrate an interference method to determine the low-energy elastic scattering amplitudes of a quantum gas. We linearly accelerate two ultracold atomic clouds up to energies of 1.2 mK and observe the collision halo by direct imaging in free space. From the interference between s- and d- partial waves in the differential scattering pattern we extract the corresponding phase shifts. The method does not require knowledge of the atomic density. This allows us to infer accurate values for the s- and d-wave scattering amplitudes from the zero-energy limit up to the first Ramsauer minimum using only the van der Waals C6 coefficient as theoretical input. For the 87Rb triplet potential, the method reproduces the scattering length with an accuracy of 6%.

Optically induced lensing effect on a Bose-Einstein condensate expanding in a moving lattice

We report the experimental observation of a lensing effect on a Bose-Einstein condensate expanding in a moving 1D optical lattice. The effect of the periodic potential can be described by an effective mass dependent on the condensate quasimomentum. By changing the velocity of the atoms in the frame of the optical lattice, we induce a focusing of the condensate along the lattice direction. The experimental results are compared with the numerical predictions of an effective 1D theoretical model. In addition, a precise band spectroscopy of the system is carried out by looking at the real-space propagation of the atomic wave packet in the optical lattice.

Levinson-like theorem for scattering from a Bose-Einstein condensate

A relation between the number of bound elementary excitations of an atomic Bose-Einstein condensate and the phase shift of elastically scattered atoms is derived. Within the Bogoliubov model of a weakly interacting Bose gas this relation is exact and generalizes Levinson's theorem. Specific features of the Bogoliubov model such as complex energy and continuum bound states are discussed and a numerical example is given.

Amplification of local instabilities in a Bose-Einstein condensate with attractive interactions

We study the collapse of large homogeneous Bose-Einstein condensates due to intrinsic attractive interactions. We observe the amplification of a local instability by seeding a momentum state p and suddenly switching the scattering length negative via a Feshbach resonance. We also observe the appearance of atoms in the conjugate momentum state as required by momentum conservation. For large condensates, the time scale for this depletion process becomes faster than that for global collapse.

Feshbach-resonance-induced atomic filamentation and quantum pair correlation in atom-laser-beam propagation

We study the propagation of an atom laser beam through a spatial region with a magnetic field tuned around a Feshbach resonance. Magnetic fields below the resonance produce an effective focusing Kerr medium that causes a modulational instability of the atomic beam. Under appropriate circumstances, this results in beam breakup and filamentation seeded by quasiparticle fluctuations and in the generation of correlated atomic pairs.

Coherent collisions between Bose-Einstein condensates

We study the nondegenerate parametric amplifier for matter waves, implemented by colliding two Bose-Einstein condensates. The coherence of the amplified waves is shown by observing high contrast interference with a reference wave and by reversing the amplification process. Since our experiments also place limits on all known sources of decoherence, we infer that relative number squeezing is most likely present between the amplified modes. Finally, we suggest that reversal of the amplification process may be used to detect relative number squeezing without requiring subshot-noise detection.

Coherence with atoms

The past decade has seen dramatic progress in our ability to manipulate and coherently control the motion of atoms. This progress has both fundamental and applied importance. On the one hand, recent experiments are providing new perspectives for the study of quantum phase transitions and highly entangled quantum states. On the other hand, this exquisite control offers the prospect of a new generation of force sensors of unprecedented sensitivity and accuracy.