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Register a new userTopological Nonlinear Optics with Spin-Orbit coupled Bose-Einstein Condensate in Cavity
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We report topological nonlinear optics with spin-orbit coupled Bose-Einstein condensate in a cavity. The cavity is driven by a pump laser and weak probe laser which excite Bose-Einstein condensate to an intermediate storage level, where the standard Raman process engineers spin-orbit coupling. We show that the nonlinear photonic interactions at the transitional pathways of dressed states result in new type of optical transparencies, which get completely inverted with atom induced gain. These nonlinear interactions also implant topological sort of features in probe transmission modes by inducing gapless Dirac-like cones, which become gaped in presence of Raman detuning. The topological features get interestingly enhanced in gain regime where the gapless topological edge-like states emerge among the probe modes, which can cause non-trivial phase transition. We show that spin-orbit coupling and Zeeman field effects also impressively revamp fast and slow probe light. The manipulation of dressed states for quantum nonlinear optics with topological characteristics in our findings could be a crucial step towards topological quantum computation.
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We present a general theory for calculating the damping rate of elementary density wave excitations in a Bose-Einstein condensate strongly coupled to a single radiation field mode of an optical cavity. Thereby we give a detailed derivation of the huge resonant enhancement in the Beliaev damping of a density wave mode, predicted recently by Konya et al., Phys.~Rev.~A 89, 051601(R) (2014). The given density-wave mode constitutes the polariton-like soft mode of the self-organization phase transition. The resonant enhancement takes place, both in the normal and ordered phases, outside the critical region. We show that the large damping rate is accompanied by a significant frequency shift of this polariton mode. Going beyond the Born-Markov approximation and determining the poles of the retarded Greens function of the polariton, we reveal a strong coupling between the polariton and a collective mode in the phonon bath formed by the other density wave modes.
We study quasiparticle scattering effects on the dynamics of a homogeneous Bose-Einstein condensate of ultracold atoms coupled to a single mode of an optical cavity. The relevant excitations, which are polariton-like mixed excitations of photonic and atomic density-wave modes, are identified. All the first-order correlation functions are presented by means of the Keldysh Greens function technique. Beyond confirming the existence of the resonant enhancement of Beliaev damping, we find a very structured spectrum of fluctuations. There is a spectral hole burning at half of the recoil frequency reflecting the singularity of the Beliaev scattering process. The effects of the photon-loss dissipation channel and that of the Beliaev damping due to atom-atom collisions can be well separated. We show that the Beliaev process does not influence the properties of the self-organization criticality.
The dispersive interaction of a Bose-Einstein condensate with a single mode of a high-finesse optical cavity realizes the radiation pressure coupling Hamiltonian. In this system the role of the mechanical oscillator is played by a single condensate excitation mode that is selected by the cavity mode function. We study the effect of atomic s-wave collisions and show that it merely renormalizes parameters of the usual optomechanical interaction. Moreover, we show that even in the case of strong harmonic confinement---which invalidates the use of Bloch states---a single excitation mode of the Bose-Einstein condensate couples significantly to the light field, that is the simplified picture of a single mechanical oscillator mode remains valid.
We propose a novel type of composite light-matter magnetometer based on a transversely driven multi-component Bose-Einstein condensate coupled to two distinct electromagnetic modes of a linear cavity. Above the critical pump strength, the change of the population imbalance of the condensate caused by an external magnetic field entails the change of relative photon number of the two cavity modes. Monitoring the cavity output fields thus allows for nondestructive measurement of the magnetic field in real time. We show that the sensitivity of the proposed magnetometer exhibits Heisenberg-like scaling with respect to the atom number. For state-of-the-art experimental parameters, we calculate the lower bound on the sensitivity of such a magnetometer to be of the order of fT/$sqrt{mathrm{Hz}}$--pT/$sqrt{mathrm{Hz}}$ for a condensate of $10^4$ atoms with coherence times of the order of several ms.
We study the spin squeezing in a spin-1/2 Bose-Einstein condensates (BEC) with Raman induced spin-orbit coupling (SOC). Under the condition of two-photon resonance and weak Raman coupling strength, the system possesses two degenerate ground states, using which we construct an effective two-mode model. The Hamiltonian of the two-mode model takes the form of the one-axis-twisting Hamiltonian which is known to generate spin squeezing. More importantly, we show that the SOC provides a convenient control knob to adjust the spin nonlinearity responsible for spin squeezing. Specifically, the spin nonlinearity strength can be tuned to be comparable to the two-body density-density interaction, hence is much larger than the intrinsic spin-dependent interaction strength in conventional two-component BEC systems such as $^{87}$Rb and $^{23}$Na in the absence of the SOC. We confirm the spin squeezing by carrying out a fully beyond-mean-field numerical calculation using the truncated Wigner method. Additionally, the experimental implementation is also discussed.
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