Bogoliubov atom pairs: revealing the interplay of quantum fluctuations and interactions in a Bose gas

David Clément

Antoine Ténart, Gaétan Hercé, Jan‐Philipp Bureik +2 more

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)

Xiaoling Cui

We investigate the effects of quantum fluctuations in a parity-time $(\mathcal{PT})$ symmetric two-species Bose-Einstein condensate (BEC). It is found that the $\mathcal{PT}$ symmetry, though preserved by the macroscopic condensate, can be spontaneously broken by its Bogoliubov quasiparticles under quantum fluctuations. The associated $\mathcal{PT}$-breaking transitions in the Bogoliubov spectrum can be conveniently tuned by the interaction anisotropy in spin channels and the strength of $\mathcal{PT}$ potential. In the $\mathcal{PT}$-unbroken regime, the real Bogoliubov modes are generally gapped, in contrast to the gapless phonon mode in Hermitian case. Moreover, the presence of $\mathcal{PT}$ potential is found to enhance the mean-field collapse and thereby intrigue the droplet formation after incorporating the repulsive force from quantum fluctuations. These remarkable interplay effects of $\mathcal{PT}$ symmetry and interaction can be directly probed in cold atoms experiments, which shed light on related quantum phenomena in general $\mathcal{PT}$-symmetric systems.

Maxim Kagan

Omar Almonajed, M. Iskin, Mehmet Özgür Oktel

Two-component bosonic droplets are commonly described within Bogoliubov theory, where beyond-mean-field quantum fluctuations stabilize the system against mean-field collapse. In the interaction regime where droplets form, however, the Bogoliubov excitation spectrum contains an imaginary branch associated with the underlying instability, which is typically omitted when evaluating the beyond-mean-field energy. Bosonic pairing theory provides an alternative description with a fully real excitation spectrum. In this work, we reformulate bosonic pairing theory within an operator formalism, making its underlying approximations transparent, and compare its predictions with those of Bogoliubov theory for a homonuclear binary Bose mixture across the crossover from a weakly interacting gas to the droplet regime. Working at fixed particle density, we determine the variational parameters of bosonic pairing theory self-consistently and focus on the regime in which both theories possess real excitation spectra, allowing a direct comparison. We find that bosonic pairing theory yields a lower grand potential than Bogoliubov theory and predicts qualitatively distinct correlation signatures, including enhanced long-wavelength interspecies momentum-space correlations and a finite density static structure factor at experimentally accessible low momenta. These differences persist over a broad range of interaction strengths and suggest that correlation and structure-factor measurements can provide direct experimental tests of bosonic pairing across the gas-to-droplet crossover.