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arXiv:1610.09076 · Physical Review A

Damping-free collective oscillations of a driven two-component Bose gas in optical lattices

Gavriil Shchedrin, Daniel Jaschke, Lincoln D. Carr

Published Apr 2, 2018• 1 citation
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Abstract

We explore the quantum many-body physics of a driven Bose-Einstein condensate in optical lattices. The laser field induces a gap in the generalized Bogoliubov spectrum proportional to the effective Rabi frequency. The lowest-lying modes in a driven condensate are characterized by zero group velocity and nonzero current. Thus, the laser field induces roton modes, which carry interaction in a driven condensate. We show that collective excitations below the energy of the laser-induced gap remain undamped, while above the gap they are characterized by a significantly suppressed Landau damping rate.

DOI
10.1103/physreva.97.043601

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We explore the quantum many-body physics of a driven Bose-Einstein condensate in optical lattices. The laser field induces a gap in the generalized Bogoliubov spectrum proportional to the effective Rabi frequency. The lowest-lying modes in a driven condensate are characterized by zero group velocity and nonzero current. Thus, the laser field induces roton modes, which carry interaction in a driven condensate. We show that collective excitations below the energy of the laser-induced gap remain undamped, while above the gap they are characterized by a significantly suppressed Landau damping rate.
We explore the quantum many-body physics of a three-component Bose-Einstein condensate in an optical lattice driven by laser fields in V and Λ configurations. We obtain exact analytical expressions for the energy spectrum and amplitudes of elementary excitations, and discover symmetries among them. We demonstrate that the applied laser fields induce a gap in the otherwise gapless Bogoliubov spectrum. We find that Landau damping of the collective modes above the energy of the gap is carried by laser-induced roton modes and is considerably suppressed compared to the phonon-mediated damping endemic to undriven scalar condensates.
We study the damping of the collective excitations of Bose-Einstein condensates in a harmonic trap potential loaded in an optical lattice. In the presence of a confining potential the system is inhomogeneous and the collective excitations are characterized by a set of discrete confined phononlike excitations. We derive a general convenient analytical description for the damping rate, which takes into account the trapping potential and the optical lattice for the Landau and Beliaev processes at any temperature TTT. At high temperature or weak spatial confinement, we show that both mechanisms display a linear dependence on TTT. In the quantum limit, we find that the Landau damping is exponentially suppressed at low temperatures and the total damping is independent of TTT. Our theoretical predictions for the damping rate under the thermal regime is in complete correspondence with the experimental values reported for the one-dimensional (1D) condensate of sodium atoms. We show that the laser intensity can tune the collision process, allowing a resonant effect for the condensate lifetime. Also, we study the influence of the attractive or repulsive nonlinear terms on the decay rate of the collective excitations. A general expression for the renormalized Goldstone frequency is obtained as a function of the 1D nonlinear self-interaction parameter, laser intensity, and temperature.
We investigate the Beliaev damping of gapped excitations in a homogenous two-component Bose-Einstein condensate with Rabi coupling and find different damping behavior of gapped excitations in two quantum phases. In the paramagnetic phase, due to constraints imposed by the Z2{\mathbb{Z}}_{2}Z2​ symmetry and energy-momentum conservation, the only damping channel available, that of decaying into one phonon and one new gapped mode, cannot occur unless the group velocity of the gapped modes surpasses the sound speed. Conversely, in the ferromagnetic phase, three distinct decay channels exist. Once the momentum of the excitations falls below a critical threshold, only one of these channels, that of decaying into two gapless modes, is activated, and the damping rate remains finite even at zero momentum.
The dynamics of a Bose-Einstein condensate in a harmonic trap with a nonadiabatically loaded optical lattice is studied analytically. As the global effect of the optical potential can be described in terms of a renormalized interaction coupling constant and of an effective mass in the laser direction, a fast loading can be understood as a sudden change of those characteristic parameters. In this approach, a standard scaling transformation is applied to study the resulting dynamics, in particular, the generation of collective modes. The relevance of the excited modes to the interference patterns obtained after free expansion is analyzed. The applicability of trap-frequency adjustments as a strategy for suppressing the loading induced excitations is discussed.
Bose–Einstein condensation represents a quintessential manifestation of quantum mechanics at macroscopic scales, where a dilute gas of bosonic atoms undergoes a phase transition to form a coherent matter wave. This study presents a comprehensive theoretical investigation of collective excitations and critical phenomena in interacting Bose–Einstein condensates (BECs). Beginning with the Gross–Pitaevskii equation , we develop the Bogoliubov theory of excitations yielding the spectrum , where is the free-particle energy and characterizes contact interactions. The spectrum reveals phonon behavior at low momenta with sound velocity , transitioning to free-particle dispersion at momenta exceeding the inverse healing length . Collective modes in harmonically trapped condensates are analyzed in the Thomas–Fermi regime, yielding breathing mode frequency and quadrupole frequency . Damping mechanisms including Landau damping ( ) and Beliaev damping ( ) are characterized. The Lee–Huang–Yang correction extends the equation of state beyond mean field. Critical phenomena near are analyzed within the 3D XY universality class, with critical exponents , , and the interaction-induced shift with . All predictions show excellent agreement with experimental measurements on ultracold atomic gases.
We study the normal mode splitting in a system consisting of a Bose–Einstein condensates (BECs) trapped inside a Fabry–Pérot cavity driven by a single mode laser field. We analyze the variations in frequency and damping rate of the collective density excitation of a BEC imparted by the optical field. We study the occurrence of normal mode splitting which appears as consequences of the hybridization of the fluctuations of the intracavity field and the condensate mode. It is shown that normal mode splitting vanishes for weak coupling between the condensate mode and the intracavity field. Moreover, we investigate the normal mode splitting in the transmission spectrum of the cavity field.