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Scientific Reports

Spin and field squeezing in a spin-orbit coupled Bose-Einstein condensate

Yixiao Huang, Zheng-Da Hu

Published Jan 26, 2015• 14 citations
Publisher

Abstract

Recently, strong spin-orbit coupling with equal Rashba and Dresselhaus strength has been realized in neutral atomic Bose-Einstein condensates via a pair of Raman lasers. In this report, we investigate spin and field squeezing of the ground state in spin-orbit coupled Bose-Einstein condensate. By mapping the spin-orbit coupled BEC to the well-known quantum Dicke model, the Dicke type quantum phase transition is presented with the order parameters quantified by the spin polarization and occupation number of harmonic trap mode. This Dicke type quantum phase transition may be captured by the spin and field squeezing arising from the spin-orbit coupling. We further consider the effect of a finite detuning on the ground state and show the spin polarization and the quasi-momentum exhibit a step jump at zero detuning. Meanwhile, we also find that the presence of the detuning enhances the occupation number of harmonic trap mode, while it suppresses the spin and the field squeezing.

DOI
10.1038/srep08006

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Recently, strong spin-orbit coupling with equal Rashba and Dresselhaus strength has been realized in neutral atomic Bose-Einstein condensates via a pair of Raman lasers. In this report, we investigate spin and field squeezing of the ground state in spin-orbit coupled Bose-Einstein condensate. By mapping the spin-orbit coupled BEC to the well-known quantum Dicke model, the Dicke type quantum phase transition is presented with the order parameters quantified by the spin polarization and occupation number of harmonic trap mode. This Dicke type quantum phase transition may be captured by the spin and field squeezing arising from the spin-orbit coupling. We further consider the effect of a finite detuning on the ground state and show the spin polarization and the quasi-momentum exhibit a step jump at zero detuning. Meanwhile, we also find that the presence of the detuning enhances the occupation number of harmonic trap mode, while it suppresses the spin and the field squeezing.
Abstract We study the spin-field and the spin-spin entanglement in the ground state of a spin-orbit coupled Bose–Einstein condensate. It is found that the spin-field and the spin-spin entanglement can be induced by the spin-orbit coupling. By mapping the system to the Dicke-like model, the system exhibits a quantum phase transition from a normal (spin balanced) phase to superradiant (spin polarized) phase. The Dicke-like phase transition can be captured by the spin-field and the spin-spin entanglement arising from the spin-orbit coupling. The spin-field and the spin-spin entanglement increase as the Raman coupling increases in the superradiant phase, while they decrease with the Raman coupling increasing in the normal phase. We also consider the effect of a finite detuning on these entanglement show that the presence of the detuning suppresses the spin-field and the spin-spin entanglement.
In recent pioneer experiment, a strong spin-orbit coupling, with equal Rashba and Dresselhaus strengths, has been created in a trapped Bose-Einstein condensate. Moreover, many exotic superfluid phenomena induced by this strong spin-orbit coupling have been predicted. In this report, we show that this novel spin-orbit coupling has important applications in quantum metrology, such as spin squeezing. We first demonstrate that an effective spin-spin interaction, which is the heart for producing spin squeezing, can be generated by controlling the orbital degree of freedom (i.e., the momentum) of the ultracold atoms. Compared with previous schemes, this realized spin-spin interaction has advantages of no dissipation, high tunability, and strong coupling. More importantly, a giant squeezing factor (lower than -30 dB) can be achieved by tuning a pair of Raman lasers in current experimental setup. Finally, we find numerically that the phase factor of the prepared initial state affects dramatically on spin squeezing.
We study the role of coupling parameters on the ground state phases of spin-orbit coupled Bose-Einstein condensates with an equal combination of Rashba and Dresselhaus coupling strength with Rabi mixing using quasi-one-dimensional coupled Gross-Pitaevskii equations. By considering weak repulsive inter- and intra-species interactions between the condensate atoms, we investigate the contribution of spin-orbit and Rabi coupling parameters on the phases. We find that for a finite Rabi coupling strength, the system undergoes a phase transition from double plane-wave phase to stripe wave phase at a critical spin-orbit coupling strength.
We investigate the transitions of ground states induced by zero momentum (ZM) coupling in pseudospin-1/2 Rashba spin-orbit coupled Bose-Einstein condensates confined in a harmonic trap. In a weak harmonic trap, the condensate presents a plane wave (PW) state, a stripe state or a spin polarized ZM state, and the particle distribution of the stripe state is weighted equally at two points in the momentum space without ZM coupling. The presence of ZM coupling induces an imbalanced particle distribution in the momentum space, and leads to the decrease of the amplitude of the stripe state. When its strength exceeds a critical value, the system experiences the transition from stripe phase to PW phase. The boundary of these two phases is shifted and a new phase diagram spanned by the ZM coupling and the interatomic interactions is obtained. The presence of ZM coupling can also achieve the transition from ZM phase to PW phase. In a strong harmonic trap, the condensate exhibits a vortex lattice state without ZM coupling. For the positive effective Rabi frequency of ZM coupling, the condensate is driven from a vortex lattice state to a vortex-free lattice state and finally to a PW state with the increase of coupling strength. In addition, for the negative effective Rabi frequency, the condensate is driven from a vortex lattice state to a stripe state, and finally to a PW state. The stripe state found in the strong harmonic trap is different from that in previous works because of its nonzero superfluid velocity along the stripes. We also discuss the influences of the ZM coupling on the spin textures, and indicate that the spin textures are squeezed transversely by the ZM coupling.
Spin-orbit coupling (SOC), the intrinsic interaction between a particle spin and its motion, is responsible for various important phenomena, ranging from atomic fine structure to topological condensed matter physics. The recent experimental breakthrough on the realization of SOC for ultra-cold atoms provides a completely new platform for exploring spin-orbit coupled superfluid physics. However, the SOC strength in the experiment is not tunable. In this report, we propose a scheme for tuning the SOC strength through a fast and coherent modulation of the laser intensities. We show that the many-body interaction between atoms, together with the tunable SOC, can drive a quantum phase transition (QPT) from spin-balanced to spin-polarized ground states in a harmonic trapped Bose-Einstein condensate (BEC), which resembles the long-sought Dicke QPT. We characterize the QPT using the periods of collective oscillations of the BEC, which show pronounced peaks and damping around the quantum critical point.
We consider a spin-orbit coupled configuration of spin-1/2 interacting bosons with equal Rashba and Dresselhaus couplings. The phase diagram of the system at T=0 is discussed with special emphasis on the role of the interaction treated in the mean-field approximation. For a critical value of the density and of the Raman coupling we predict the occurrence of a characteristic tricritical point separating the spin mixed, the phase separated, and the zero momentum states of the Bose gas. The corresponding quantum phases are investigated analyzing the momentum distribution, the longitudinal and transverse spin polarization, and the emergence of density fringes. The effect of harmonic trapping as well as the role of the breaking of spin symmetry in the interaction Hamiltonian are also discussed.