We explore the possibility of detecting many-body entanglement using time-of-flight (TOF) momentum correlations in ultracold atomic Fermi gases. In analogy to the vacuum correlations responsible for Bekenstein-Hawking black hole entropy, a partitioned atomic gas will exhibit particle-hole correlations responsible for entanglement entropy. The signature of these momentum correlations might be detected by a sensitive TOF-type experiment.
We explore the possibility of detecting many-body entanglement using time-of-flight (TOF) momentum correlations in ultracold atomic Fermi gases. In analogy to the vacuum correlations responsible for Bekenstein-Hawking black hole entropy, a partitioned atomic gas will exhibit particle-hole correlations responsible for entanglement entropy. The signature of these momentum correlations might be detected by a sensitive TOF-type experiment.
Momentum space entanglement entropy probes quantum correlations in interacting fermionic phases. It is very sensitive to interactions, obeying volume-law scaling in general, while vanishing in the Fermi gas. We show that the R\'enyi entropy in momentum space has a systematic expansion in terms of the phase space volume of the partition, which holds at all orders in perturbation theory. This permits, for example, the controlled computation of the entropy of thin shells near the Fermi wave vector in isotropic Fermi liquids and BCS superconductors. In the Fermi liquid, the thin-shell entropy is a universal function of the quasiparticle residue. In the superconductor, it reflects the formation of Cooper pairs. Momentum space R\'enyi entropies are accessible in cold atomic and molecular gas experiments through a time-of-flight generalization of previously implemented measurement protocols.
Many-body interference between indistinguishable particles can give rise to strong correlations rooted in quantum statistics. We study such Hanbury Brown-Twiss-type correlations for number states of ultracold massive fermions. Using deterministically prepared ^{6}Li atoms in optical tweezers, we measure momentum correlations using a single-atom sensitive time-of-flight imaging scheme. The experiment combines on-demand state preparation of highly indistinguishable particles with high-fidelity detection, giving access to two- and three-body correlations in fields of fixed fermionic particle number. We find that pairs of atoms interfere with a contrast close to 80%. We show that second-order density correlations arise from contributions from all two-particle pairs and detect intrinsic third-order correlations.
Ultracold atoms in optical lattices provide an extremely clean and controllable setting to explore quantum many-body phases of matter. Here we give a brief review of the strong-correlation physics that has been realized using such ultracold atoms in optical lattices ranging from the realization of Hubbard models to studies of quantum magnetism and the detection of single atoms with lattice site resolution. All this has opened up fundamentally new opportunities for the investigation of quantum many-body systems. Introduction Over the past years, ultracold atoms in optical lattices have emerged as versatile new systems to explore the physics of quantum many-body systems. On the one hand, they can be helpful in gaining a better understanding of known phases of matter and their dynamical behavior; on the other hand, they allow one to realize completely novel quantum systems that have not been studied before in nature [1, 2, 3]. Commonly, the approach of exploring quantum many-body systems in such a way is referred to as “quantum simulations.” Examples of some of the first strongly interacting many-body phases that have been realized both in lattices and in the continuum include the quantum phase transition from a superfluid to a Mott insulator [4, 5, 6], fermionic Mott insulators [7, 8], the achievement of a Tonks- Girardeau gas [9, 10], and the realization of the Bose-Einsten condensate (BEC)– Bardeen-Cooper-Schrieffer (BCS) crossover (see also Chapter 12) in Fermi gas mixture [11] using Feshbach resonances [12]. In almost all of these experiments, detection was limited to time-of-flight imaging or more refined derived techniques that mainly characterized the momentum distribution of the quantum gas [2]. For several years, researchers in the field have therefore aspired to employ in situ single-particle detection methods for the analysis of ultracold quantum gases. Only recently has it become possible to implement such imaging techniques, marking a milestone for the characterization and manipulation of ultracold quantum gases [13, 14, 15, 16, 17]. In our discussion, we will focus on one of the most successful of these techniques based on high-resolution fluorescence imaging. Despite being a rather new technique, such quantum gas microscopy has already proven to be an enabling technology for probing and manipulating quantum many-body systems. For the first time, controllable and strongly interacting many-body systems, as realized with ultracold atoms, could be observed on a local scale [17, 16].
We propose a detection method for ultracold atoms which allows reconstruction of the full one-particle and two-particle correlation functions from the measurements. The method is based on Fourier sampling of the time-of-flight images through two consecutive impulsive Raman pulses. For applications of this method, we discuss a few examples, including detection of phase separation between superfluid and Mott insulators, various types of spin or superfluid orders, entanglement, exotic or fluctuating orders.
Multiparticle entangled states, essential ingredients for modern quantum technologies, are routinely generated in experiments of atomic Bose-Einstein condensates (BECs). However, the entanglement in ultracold interacting Fermi gases has not been yet exploited. In this work, by using an ansatz of composite bosons, we show that many-particle entanglement between two fermionic ensembles localized in spatially separated modes can be generated by splitting an ultracold interacting Fermi gas in the (molecular) BEC regime. This entanglement relies on the fundamental fermion exchange symmetry of molecular constituents and might be used for implementing quantum applications in oncoming experiments. We show that the generated fermionic ensembles can be highly entangled and exhibit nonlocal quantum correlations. Entanglement-induced suppression of fluctuations in the single-fermion spectral density of the ultracold fermionic gas is also observed.
We investigate quantum correlations in the ground state of noninteracting Fermi gases of N particles trapped by an external space-dependent harmonic potential, in any dimension. For this purpose we compute one-particle correlations, particle fluctuations, and bipartite entanglement entropies of extended space regions, and study their large-N scaling behaviors. The half-space von Neumann entanglement entropy is computed for any dimension, obtaining ${S}_{\mathrm{HS}}\ensuremath{\approx}{c}_{l}{N}^{(d\ensuremath{-}1)/d}\mathrm{ln}N$ analogously to homogenous systems, with cl=1/6,1/(62),1/(66) in one, two, and three dimensions, respectively. We show that the asymptotic large-N relation ${S}_{A}\ensuremath{\approx}{\ensuremath{\pi}}^{2}{V}_{A}/3$, between the von Neumann entanglement entropy SA and particle variance VA of an extended space region A, holds for any subsystem A and in any dimension, analogously to homogeneous noninteracting Fermi gases.