We study a highly efficient, matter-wave amplification mechanism in a longitudinally-excited, Bose-Einstein condensate and reveal a very large enhancement due to nonlinear gain from a sixmatter- optical, wave-mixing process involving four photons. Under suitable conditions this opticallydegenerate, four-photon process can be stronger than the usual two-photon inelastic light scattering mechanism, leading to nonlinear growth of the observed matter-wave scattering independent of any enhancement from bosonic stimulation. Our theoretical framework can be extended to encompass even higher-order, nonlinear superradiant processes that result in higher-order momentum transfer.
The advent of the laser as an intense, coherent light source gave birth to nonlinear optics, which now plays an important role in many areas of science and technology. One of the first applications of nonlinear optics was the production of coherent light of a new frequency by multi-wave mixing of several optical fields in a nonlinear medium. Until the experimental realization of Bose-Einstein Condensation (BEC) there had been no intense coherent source of matter-waves analogous to the optical laser. BEC has already been exploited to produce a matter-wave 'laser' atom optics was reported: the observation of coherent four wave mixing in which three sodium matter waves mix to produce a fourth. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose- Einstein condensate. The high-momentum components and the remaining zero momentum condensate component interact to form a new momentum component due to the nonlinear self- interaction of the bosonic atoms. We develop a quantum mechanical description, based on the slowly-varying-envelope approximation to the time-dependent nonlinear Schroedinger equation, to describe four-wave mixing in Bose-Einstein condensates and apply this description to understand the experimental observations and to make new predictions. We examine the role of phase-modulation, momentum and energy conservation, and particle number conservation in four-wave mixing of matter waves.
We study the properties of Bose–Einstein condensates under a non-Hermitian spin–orbit coupling (SOC), induced by a dissipative two-photon Raman process. We focus on the dynamics of the condensate at short times, when the impact of decoherence induced by quantum jumps is negligible and the dynamics is coherently driven by a non-Hermitian Hamiltonian. Given the significantly modified single-particle physics by dissipative SOC, the interplay of non-Hermiticity and interaction leads to a quasi-steady-state phase diagram different from its Hermitian counterpart. In particular, we find that dissipation can induce a phase transition from the stripe phase to the plane-wave phase. We further map out the phase diagram with respect to the dissipation and interaction strengths, and finally investigate the stability of quasi-steady states through the time-dependent dissipative Gross–Pitaevskii equation. Our results are readily accessible based on standard experiments with synthetic spin–orbit couplings.
A recent experiment [Deng et al., Nature (London) 398, 218 (1999)] demonstrated four-wave mixing of matter wave packets created from a Bose-Einstein condensate. The experiment utilized light pulses to create two high-momentum wave packets via Bragg diffraction from a stationary Bose-Einstein condensate. The high-momentum components and the initial low-momentum condensate interact to form a new momentum component due to the nonlinear self-interaction of the bosonic atoms. We develop a three-dimensional quantum- mechanical description, based on the slowly-varying-envelope approximation, for four-wave mixing in Bose-Einstein condensates using the time-dependent Gross-Pitaevskii equation. We apply this formulation to describe the experimental observations and to make predictions. We examine the role of phase-modulation, momentum, and energy conservation (i.e., phase matching), and particle number conservation in four-wave mixing of matter waves, and develop simple models for understanding our numerical results.
The advent of the laser as an intense, coherent light source gave birth to nonlinear optics, which now plays an important role in many areas of science and technology. One of the first applications of nonlinear optics was the production of coherent light of a new frequency by multi-wave mixing of several optical fields in a nonlinear medium. Until the experimental realization of Bose-Einstein Condensation (BEC) there had been no intense coherent source of matter-waves analogous to the optical laser. FEC has already been exploited to produce a matter-wave `laser' leading to the threshold of a new field of physics: nonlinear atom optics. Recently the first experiment in nonlinear atom optics was reported: the observation of coherent four wave mixing in which three sodium matter waves mix to produce a fourth. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose- Einstein condensate. The high-momentum components and the remaining zero momentum condensate component interact to form a new momentum component due to the nonlinear self- interaction of the bosonic atoms. We develop a quantum mechanical description, based on the slowly-varying-envelope approximation to the time-dependent nonlinear Schrodinger equation (also called the Gross-Pitaevskii equation), to describe four-wave mixing in Bose-Einstein condensates and apply this description to understand the experimental observations and to make new predictions. We examine the role of phase-modulation, momentum and energy conservation (i.e., phase-matching), and particle number conservation in four-wave mixing of matter waves.
The interplay of non-Hermiticity and spin-orbit (SO) coupling has attracted great interest in condensed-matter physics, ultracold atomic physics, optics, and other fields. Here we study the ground states, collective modes, and free-expansion dynamics of non-Hermitian SO-coupled Bose-Einstein condensates (BECs) with momentum-dependent gain and loss in a harmonic trap. An efficient analytical method for revealing the impact of non-Hermiticity on the ground states and dynamics of SO-coupled BECs is proposed. A dispersion relation with effective mass
m2 that can be larger than 1, less than 1, or negative is engineered by the momentum-dependent gain and loss, which is distinct from the ordinary SO-coupled BECs, where
m2>1 always holds. Negative effective mass can lead to the self-interference effect of condensates, while
m2<1 means that condensates can gain a larger acceleration when they are subjected to a constant force. Interestingly, the high-order zero-point kinetic energies are derived analytically and confirmed numerically, establishing a link between the zero-point kinetic energy and dispersion relation. In particular, the second-order zero-point kinetic energy can be controlled by the effective mass
m2, which has an important impact on many phenomena of ultracold atomic physics. In addition, another key result is that the frequencies of dipole and breathing modes can exceed the values of traditional BECs without SO coupling when the effective mass
m2<1, showing that gain (loss) is a powerful tool for probing and controlling quantum systems. Moreover, the asymmetric free expansion and self-interference effect of the condensates caused by negative effective masses are observed, and it is found that the rate of expansion is controlled by the effective mass
m2. Our results show that the controllable gain-loss engineering in SO-coupled BECs provides a prospect to explore novel quantum many-body physics.