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Journal of Atomic Molecular Condensate and Nano Physics

Study of the Effect of Artificial Gauge Field on the Supersolid Phase in Cold Atomic Condensates

Rashi Sachdeva, Sankalpa Ghosh

Published Apr 30, 2014• 1 citation
Publisher

Abstract

Ultra cold atomic condensate with long range interaction is considered as a possible candidate to realize the supersolid phase. Such a supersolid phase can be subjected to artificial gauge field created either through rotation or by introducing space dependent coupling among hyperfine states of the atoms using Raman lasers. We study the effect of an artificial gauge field on the Supersolid phase in ultracold atomic condensates with long range interactions. Using Mean field approach, we demonstrate the structural differences between vortex in a supersolid and superfluid. We determine analytically the effect of the artificial gauge field on the density wave - supersolid (DW-SS) and the Mott insulator-superfluid (MI-SF) transition boundary. We also point out that in symmetric gauge the momentum distribution structure at these transition boundaries bears distinctive signatures of vortices in supersolid and superfluid phases. We point out that these results can clearly identify such a ultra cold atomic supersolid phase.

DOI
10.26713/jamcnp.v1i1.203

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Ultra cold atomic condensate with long range interaction is considered as a possible candidate to realize the supersolid phase. Such a supersolid phase can be subjected to artificial gauge field created either through rotation or by introducing space dependent coupling among hyperfine states of the atoms using Raman lasers. We study the effect of an artificial gauge field on the Supersolid phase in ultracold atomic condensates with long range interactions. Using Mean field approach, we demonstrate the structural differences between vortex in a supersolid and superfluid. We determine analytically the effect of the artificial gauge field on the density wave - supersolid (DW-SS) and the Mott insulator-superfluid (MI-SF) transition boundary. We also point out that in symmetric gauge the momentum distribution structure at these transition boundaries bears distinctive signatures of vortices in supersolid and superfluid phases. We point out that these results can clearly identify such a ultra cold atomic supersolid phase.
We study the effect of an artificial gauge field on the zero-temperature phase diagram of an extended Bose-Hubbard model that describes ultracold atoms in optical lattices with long-range interactions by using strong-coupling perturbation theory. We determine analytically the effect of the artificial gauge field on the density-wave--supersolid (DW-SS) and the Mott-insulator--superfluid (MI-SF) transition boundary. The momentum distribution at these two transition boundaries is also calculated in this approach. It is shown that such a momentum distribution, which can be observed in time-of-flight measurements, reveals the symmetry of the gauge potential through the formation of a magnetic Brillouin zone and clearly distinguishes between the DW-SS and MI-SF boundary. We also point out that, in a symmetric gauge, the momentum distribution structure at these transition boundaries bears distinctive signatures of vortices in supersolid and superfluid phases.
Abstract Within the mean field Gross–Pitaevskii framework, ultracold atomic condensates with long-range interaction are predicted to have a supersolid-like ground state beyond a critical interaction strength. Such a mean field supersolid-like ground state has periodically modulated superfluid density which implies the coexistence of superfluid and crystalline order. An ultracold atomic system in such a mean field ground state can be subjected to an artificial gauge field created either through rotation or by introducing space dependent coupling among hyperfine states of the atoms using Raman lasers. Starting from this Gross–Pitaevskii energy functional that describes such systems at zero temperature, we construct a hydrodynamic theory to describe the low-energy long-wavelength excitations of a rotating supersolid of weakly interacting ultracold atoms in two spatial dimensions for a generic type of long-range interaction. We treat the supersolidity in such a system within the framework of the well known two-fluid approximation. Considering such a system in the fast rotation limit where a vortex lattice in superfluid coexists with the supersolid lattice, we analytically obtain the dispersion relations of collective excitations around this equilibrium state. The dispersion relation gives the modes of the rotating supersolid which can be experimentally measured within the current technology. We point out that this can clearly identify an ultracold atomic supersolid phase in an unambiguous way.
Abstract Ultra cold atomic condensate with long range interaction is considered as a possible candidateto realize the supersolid phase. Such a supersolid phase can be subjected to arti cial gauge eldcreated either through rotation or by introducing space dependent coupling among hyper ne statesof the atoms using Raman lasers. We construct a Gross-Pitaevskii hydrodynamic theory to describethe low energy long wavelength excitations of such rotating supersolid of weakly interacting ultracold atoms for generic type of long range interaction. We treat the supersolid within the frameworkof well known two uid approximation. We consider such system in the fast rotation limit where avortex lattice in superuid coexists with the supersolid lattice and analytically obtain the dispersionrelations of collective excitations around this equilibrium state. The dispersion relation suggests amode splitting due to the existence of two lattices which can be experimentally measured within thecurrent technology. We point out that this can clearly identify such a ultra cold atomic supersolidphase.
Quantum mechanically, static or applied gauge fields manifest themselves by directly coupling to a system's phase. Artificial gauge field techniques manipulate the phase of a Bose-Einstein condensate's order parameter, yielding effects present in condensed matter systems subject to magnetic fields, electric fields, or spin-orbit coupling. In this chapter, we explore the impact of these artificial gauge fields on Bose- Einstein condensates and explain the consequences. Several analogues to traditional condensed matter systems are enabled by these techniques, including the Hall effect, superfluid vortex nucleation in systems with artificial magnetic fields, and magnetic-like phase transitions in systems with spin-orbit coupling. Introduction Since the first experiments with Bose-Einstein condensates (BECs), researchers have exploited the universality of physical laws to draw analogies between the behavior of ultracold quantum gases and systems ranging from material to astrophysical. These analogous situations are deliberately engineered, giving cold-atom “quantum simulators” [1] that exhibit behavior either observed or predicted in analogous quantum systems. Superfluidity was one of the first many-body quantum phenomena demonstrated in BECs. For example, several experiments showed superfluid behavior by rapidly rotating the condensates and observing the formation of vortices [2, 3, 4, 5] – quantized point-defects in the BEC's order parameter. In the rotating frame of these experiments, this nucleation of vortices could be understood as the consequence of an artificial magnetic field [6] that arises via the formal equivalence of the rotating-frame Coriolis force and the Lorentz force, which we describe in Section 15.4.1. Together with other measurements, these results proved to be in excellent agreement with the predictions of the Gross-Pitaevskii equation (GPE) [7], a decades-old idealization of superfluid helium. Buoyed by the prospect for studying magnetic field–driven strongly correlated systems using these nearly ideal quantum gases, proposals for alternate techniques to simulate gauge fields were developed. These methods primarily employ an internal state–selective atom–light coupling, where the photon momentum provides the forces necessary to mimic a Lorentz force [8, 9, 10, 11, 12, 13, 14, 15, 16]. The first demonstration of this type of technique used a spatially dependent Ramantransition scheme to effect a magnetic field [17], and experiments demonstrating artificial electric fields [18] and spin-orbit coupling [19, 20, 21, 22, 23, 24] soon followed.
We examine the zero- and finite-temperature phase diagrams of soft-core bosons of the extended Bose-Hubbard model on a square optical lattice. To study various quantum phases and their transitions we employ single-site and cluster Gutzwiller mean-field theory. We have observed that the Mott insulator phase vanishes above a critical value of nearest-neighbor interaction and the supersolid phase occupies a larger region in the phase diagram. We show that the presence of an artificial gauge field enlarges the domain of the supersolid phase. The finite temperature destroys the crystalline structure of the supersolid phase and thereby favors the normal fluid--to--superfluid phase transition. The presence of an envelope harmonic potential demonstrates the coexistence of different phases, and at $z{k}_{B}T\ensuremath{\geqslant}V$, thermal energy comparable to or higher than the long-range interaction energy, the supersolidity of the system is destroyed.
Chiral superfluidity in ultracold Fermi gases represents a fascinating frontier in condensed matter physics, offering a pristine platform for exploring exotic quantum phases with topological properties. This paper provides a comprehensive review of the theoretical underpinnings and potential experimental realizations of chiral superfluids when ultracold Fermi gases are subjected to artificial gauge fields. We begin by introducing the concept of artificial gauge fields, detailing how they can be engineered using laser-atom interactions to impart synthetic spin-orbit coupling and break time-reversal symmetry, thereby creating conditions conducive to chiral order. We then delve into the microscopic theory of chiral pairing, particularly focusing on p-wave and p+ip superfluid states, which are intrinsically chiral and support topologically protected edge modes, such as Majorana fermions. The methodology section outlines the theoretical tools employed, including mean-field BCS theory and Bogoliubov-de Gennes equations, to predict the phase diagrams and spectroscopic signatures of these exotic states. We discuss the effects of varying interaction strengths, gauge field parameters, and trapping potentials on the emergence and stability of chiral phases. The potential for experimental detection through rf spectroscopy, noise correlations, and direct imaging of vortex cores is also addressed. Our findings underscore the significant potential of ultracold atomic systems as quantum simulators for unraveling the mysteries of topological phases, with profound implications for fundamental physics and quantum information science.