Single-shot imaging of trapped Fermi gas

Abstract

-Recently developed techniques allow for simultaneous measurements of the positions of all ultra cold atoms in a trap with high resolution. Each such single shot experiment detects one element of the quantum ensemble formed by the cloud of atoms. Repeated single shot measurements can be used to determine all correlations between particle positions as opposed to standard measurements that determine particle density or two-particle correlations only. In this paper we discuss the possible outcomes of such single shot measurements in case of cloud of ultra-cold noninteracting Fermi atoms. We show that the Pauli exclusion principle alone leads to correlations between particle positions that originate from unexpected spatial structures formed by the atoms.Introduction. -Tremendous progress in experimental techniques of preparing, manipulating and probing ultra-cold gases have opened new possibilities of optical methods of monitoring atomic systems. Atomic fluorescence microscopes with resolution in the range of hundreds of nanometers became accessible [1][2][3][4][5][6][7]. The microscopes allow for observation of both boson and fermion atoms with resolution comparable to the optical wavelength. Single shot pictures of such systems correspond to a single realization of the N -body probability density as opposed to a one-particle probability distribution. Difference between the two is tremendous, they differ by N body correlations. The seminal work of [8] shows how interference fringes, visible in a simultaneous single shot picture of N atoms, arise in the course of measurement. No fringes are observed in a single particle detection instead. In a similar way the solitons emerge in a process of detection of N -particles prepared in a type II excited state of a 1D system of bosons interacting via short-range potential described by the Lieb-Linger model [9]. Single shot time-dependent simulations of many-body dynamics showing appearance of fluctuating vortices and center-ofmass fluctuations of attractive BEC have been reported recently [10].

Quantum dark solitons in a Bose gas confined in a hard-wall box

“…As in Refs. [50,61] we perform Markovian walk in the configuration space. That is, by sampling N -dimensional probability distribution |Ψ(x 1 , .…”

Quantum point spread function for imaging trapped few-body systems with a quantum gas microscope

“…We remark that sampling of high-order correlations is statistically more intensive. If, however, the system possesses some symmetries, a proper pre-processing of single-shot images [25,26] will decrease the total experimental effort for accessing higher-order correlations.…”

Experimentally Accessible Invariants Encoded in Interparticle Correlations of Harmonically Trapped Ultra-cold Few-Fermion Mixtures

“…However, recent experiments allow one not only to take a 'photograph' of all ultra-cold atoms but also to measure all their positions simultaneously [45][46][47][48][49][50][51][51][52][53]. It means that, in principle, it is possible to measure manybody correlations [54]. This new tool gives another opportunity to probe theoretically predicted correlations in quantum systems and motivates us to describe closely the properties of higher correlations in few-body systems.…”