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Observation of pairs of atoms at opposite momenta in an equilibrium interacting Bose gas

Antoine Ténart, Gaétan Hercé, Jan‐Philipp Bureik, Alexandre Dareau, David Clément

Published Jun 3, 2022• 1 citation
Publisher

Abstract

Quantum fluctuations play a central role in the properties of quantum matter. In non-interacting ensembles, they manifest as fluctuations of non-commuting observables, quantified by Heisenberg inequalities. In the presence of interactions, additional quantum fluctuations appear, from which many-body correlations and entanglement originate. In the context of many-body physics, the Bogoliubov theory provides us with an illuminating microscopic picture of how this occurs for weakly-interacting bosons, with the appearance of the quantum depletion formed by pairs of bosons with opposite momenta. This conceptually simple example yet lacks experimental confirmation. Exploiting the single particle resolution of our metastable Helium detector, we report the direct observation of pairs of atoms with opposite momenta in the depletion of an equilibrium interacting Bose gas. We show that the pair correlation signal rapidly drops as temperature rises, as expected for the quantum depletion. A quantitative study of the atom-atom correlations, both at opposite and close-by momenta, allows us to fully characterise the quantum correlations in the interacting Bose gas. Our results demonstrate how an equilibrium many-body quantum state acquires specific correlations - those of two-mode squeezed states here - as a result of the interplay between quantum fluctuations and interactions. In addition, the measured amplitudes of the correlation signals reveal sub-poissonian number differences between modes at opposite momenta, an important step towards characterising entanglement in equilibrium many-body quantum states. In the future, our approach can be used to characterize more strongly correlated systems for which a theoretical description is lacking, thus fully entering the realm of quantum simulation. - A. Tenart, G. Hercé, J.-P. Bureik, A. Dareau, D. Clément, arXiv:2105:05664 - T. D. Lee, K. Huang, and C. N. Yang, Phys. Rev. 106 (1957) - R. Lopes, C. Eigen, N. Navon, D. Clément, R. P. Smith, and Z. Hadzibabic, PRL 119 (2017) - H. Cayla, C. Carcy, Q. Bouton, R. Chang, G. Carleo, M. Mancini, and D. Clément, PRA 97 (2018) - A. Tenart, C. Carcy, H. Cayla, T. Bourdel, M. Mancini and D. Clément, PRR. 2 (2020) - H. Cayla, S. Butera, C. Carcy, A. Tenart, G. Hercé, M. Mancini, A. Aspect, I. Carusotto, and D. Clément, PRL 125 (2020)

DOI
10.1117/12.2621014

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Quantum fluctuations play a central role in the properties of quantum matter. In non-interacting ensembles, they manifest as fluctuations of non-commuting observables, quantified by Heisenberg inequalities. In the presence of interactions, additional quantum fluctuations appear, from which many-body correlations and entanglement originate. In the context of many-body physics, the Bogoliubov theory provides us with an illuminating microscopic picture of how this occurs for weakly-interacting bosons, with the appearance of the quantum depletion formed by pairs of bosons with opposite momenta. This conceptually simple example yet lacks experimental confirmation. Exploiting the single particle resolution of our metastable Helium detector, we report the direct observation of pairs of atoms with opposite momenta in the depletion of an equilibrium interacting Bose gas. We show that the pair correlation signal rapidly drops as temperature rises, as expected for the quantum depletion. A quantitative study of the atom-atom correlations, both at opposite and close-by momenta, allows us to fully characterise the quantum correlations in the interacting Bose gas. Our results demonstrate how an equilibrium many-body quantum state acquires specific correlations - those of two-mode squeezed states here - as a result of the interplay between quantum fluctuations and interactions. In addition, the measured amplitudes of the correlation signals reveal sub-poissonian number differences between modes at opposite momenta, an important step towards characterising entanglement in equilibrium many-body quantum states. In the future, our approach can be used to characterize more strongly correlated systems for which a theoretical description is lacking, thus fully entering the realm of quantum simulation. - A. Tenart, G. Hercé, J.-P. Bureik, A. Dareau, D. Clément, arXiv:2105:05664 - T. D. Lee, K. Huang, and C. N. Yang, Phys. Rev. 106 (1957) - R. Lopes, C. Eigen, N. Navon, D. Clément, R. P. Smith, and Z. Hadzibabic, PRL 119 (2017) - H. Cayla, C. Carcy, Q. Bouton, R. Chang, G. Carleo, M. Mancini, and D. Clément, PRA 97 (2018) - A. Tenart, C. Carcy, H. Cayla, T. Bourdel, M. Mancini and D. Clément, PRR. 2 (2020) - H. Cayla, S. Butera, C. Carcy, A. Tenart, G. Hercé, M. Mancini, A. Aspect, I. Carusotto, and D. Clément, PRL 125 (2020)
We report the realization of a Hanbury Brown and Twiss (HBT)-like experiment with a gas of interacting bosons at low temperatures. The low-temperature regime is reached in a three-dimensional optical lattice and atom-atom correlations are extracted from the detection of individual metastable helium atoms after a long free fall. We observe, in the noncondensed fraction of the gas, a HBT bunching whose properties strongly deviate from the HBT signals expected for noninteracting bosons. In addition, we show that the measured correlations reflect the peculiar quantum statistics of atoms belonging to the quantum depletion and of the Bogoliubov phonons, i.e., of collective excitations of the many-body quantum state. Our results demonstrate that atom-atom correlations provide information about the quantum state of interacting particles, extending the interest of HBT-like experiments beyond the case of noninteracting particles.
We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-PPP representation method. This allows us to provide an exact treatment of the molecular field depletion and sss-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with nonopposite momenta. The net effect of this process---which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion---is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.
Analyzing the noise in the momentum profiles of single realizations of one-dimensional Bose gases, we present the experimental measurement of the full momentum-space density correlations ⟨δn_{p}δn_{p^{'}}⟩, which are related to the two-body momentum correlation function. Our data span the weakly interacting region of the phase diagram, going from the ideal Bose gas regime to the quasicondensate regime. We show experimentally that the bunching phenomenon, which manifests itself as super-Poissonian local fluctuations in momentum space, is present in all regimes. The quasicondensate regime is, however, characterized by the presence of negative correlations between different momenta, in contrast to the Bogolyubov theory for Bose condensates, predicting positive correlations between opposite momenta. Our data are in good agreement with ab initio calculations.
This thesis describes a collection of experiments that explore interacting ultracold Bose gases, both in and out of equilibrium. Our experiments are performed using a gas of 39^{39}39K or 87^{87}87Rb confined in the uniform potential of an optical box trap, a novel testbed for quantum many-body phenomena. Our work focuses on weakly interacting non-equilibrium systems, moderately interacting systems that are still in equilibrium, and the unitary Bose gas which is both strongly interacting and eludes equilibrium. We begin with studies of weakly-interacting gases far from equilibrium, which feature ties to nonlinear wave phenomena. Highlights of our experiments include the direct measurement of turbulent-cascade fluxes, which (alongside realizing a tuneable dissipation scale) allow us to demonstrate the zeroth law of turbulence, and the first observation of weak collapse, a general type of nonlinear wave collapse predicted over 40 years ago. We then turn to moderately strong interactions, confronting existing theories of interacting quantum fluids. One of our most important results is the first quantitative measurement of the quantum depletion of a Bose–Einstein condensate, confirming a 70-year-old theory first developed to describe liquid helium. The culmination of our work explores the unitary Bose gas, where interparticle interactions are as strong as allowed by the laws of quantum mechanics. This strongly-correlated state promises tantalizing possibilities, including emergent universal behavior set solely by the gas density and novel forms of superfluidity. However, the strong interactions also lead to a complex interplay between coherent and dissipative dynamics. By disentangling these two processes, we have caught a glimpse of the promises that the unitary Bose gas holds. In particular, we observe the emergence of universal behavior, and find that the gas features a well defined quasi-equilibrium state, with a non-zero condensed fraction.
Quantum systems consisting of many particles are both interesting from the physics and the mathematics perspective. One aspect that makes them fascinating from the physics point of view is that they can exhibit quantum effects on macroscopic scales such as Bose-Einstein condensation. This phenomenon, first predicted 100 years ago by Bose [19] and Einstein [44], occurs when a dilute gas of bosons is cooled down to very low temperatures. Below a certain critical temperature a condensate forms, meaning that a macroscopic fraction of the particles is in the same one-particle state, and thus, quantum phenomena become relevant on length scales much larger than the individual atom. The occurrence of Bose-Einstein condensation is also related to superfluidity as suggested in [88]. Bose-Einstein condensation has been achieved experimentally independently by the groups of Cornell and Wieman [3] and Ketterle [40] earning them a Nobel prize in 2001. While Bose and Einstein analyzed theoretically the non-interacting gas, an effective theory describing weakly interacting Bose gases was proposed by Bogoliubov in 1947 with the goal of explaining the occurrence of superfluidity in liquid helium [18]. Using assumptions such as that condensation indeed occurs, his theory yields predictions for the low-energy states of the system. Seen from the mathematics perspective, describing the Bose gas is an interesting challenge due to the strong correlations between particles introduced by the interaction making this case much harder to study than the non-interacting one. In particular, a proof that Bose-Einstein condensation occurs in the thermodynamic limit for continuous systems is still out of reach. However, there has been a lot of work regarding the rigorous analysis of bosonic systems in various relevant regimes. This thesis contains three new contributions establishing rigorous results on bosonic systems in different, physically relevant settings. It is based on the articles [37, 27, 31]. The first result concerns the time-evolution of initially trapped Bose gases in the ultra-dilute Gross-Pitaevskii regime. Under some assumptions on the initial data satisfied in particular by a class of states that are expected to approximate the ground state in a trap, we derive a quasi-free approximation that is close to the true solution in L2L^2L2-norm. In particular, we show that this approximate wave function is described in terms of a Bose-Einstein condensate in a one-particle state following the time-dependent Gross-Pitaevskii equation together with pair excitations with respect to this condensate. As a corollary, we establish a central limit theorem for bounded one-particle observables. The second result is a simple proof of Bose-Einstein condensation for interacting, ultra-dilute gases. More specifically, we consider scalings interpolating between the Gross-Pitaevskii regime and the thermodynamic limit. While condensation had been shown to hold in these regimes before, the advantage of the method used here is its simplicity. Lastly, the third result establishes an upper bound on the ground state energy of a dilute Bose gas in the thermodynamic limit. It captures rigorously the third order correction to the energy per unit volume for sufficiently low densities as predicted in the physics literature first by Wu and subsequently others. Full-text embargoed until: 2026-01-01\textit{Full-text embargoed until: 2026-01-01}Full-text embargoed until: 2026-01-01
This thesis presents two experiments on ultracold gases of metastable Helium that constitute the extension, to matter waves, of experiments that have been fundamental for the development of quantum optics. Both experiments have been realized by using a single atom detector, that allows one to reconstruct the position of the atoms in three dimensions. In the first experiment we directly compared the two-body correlation function for a cold cloud of identical fermions and for a cold cloud of identical bosons at the same temperature issued from the same experimental apparatus. Since bosons and fermions obey different quantum statistics, the two-body correlation functions are different: identical bosons tend to be detected bunched in pairs, while identical fermions tend to antibunch because of the Pauli exclusion principle. In the second experiment we studied the correlation between pairs of bosonic atoms generated in the collision of two Bose-Einstein condensates. The measurement of the correlation function allows us to demonstrate that atoms flying back to back in the centre of mass frame are correlated in pairs. Furthermore the observation of a Hanbury Brown Twiss correlation between atoms with collinear velocity demonstrates that our system cannot be interpreted in terms of classical mechanics, but that the bosonic statistics plays a crucial role. A new version of the experiment will allow us to measure the angular dependence of the population of the scattering modes and the number difference squeezing between two correlated modes.