We present numerical results of a one-dimensional spin–orbit coupled Bose–Einstein condensate expanding in a speckle disorder potential by employing the Gross–Pitaevskii equation. Localization properties of a spin–orbit coupled Bose–Einstein condensate in zero-momentum phase, magnetic phase and stripe phase are studied. It is found that the localizing behavior in the zero-momentum phase is similar to the normal Bose–Einstein condensate. Moreover, in both magnetic phase and stripe phase, the localization length changes non-monotonically as the fitting interval increases. In magnetic phases, the Bose–Einstein condensate will experience spin relaxation in disorder potential.We present numerical results of a one-dimensional spin–orbit coupled Bose–Einstein condensate expanding in a speckle disorder potential by employing the Gross–Pitaevskii equation. Localization properties of a spin–orbit coupled Bose–Einstein condensate in zero-momentum phase, magnetic phase and stripe phase are studied. It is found that the localizing behavior in the zero-momentum phase is similar to the normal Bose–Einstein condensate. Moreover, in both magnetic phase and stripe phase, the localization length changes non-monotonically as the fitting interval increases. In magnetic phases, the Bose–Einstein condensate will experience spin relaxation in disorder potential.

Chinese Physics BFeb 10, 20227 citations

Bose-Einstein Condensation of Non-Interacting Bosons

Fabrizio Tafuri, C. A. Perroni, G. De Filippis

UNITEXT for physicsJan 1, 20260 citations

Bose-Einstein condensates with spin and orbital angular momentum coupling

Kuei Sun, Chunlei Qu, Chuanwei Zhang

Bulletin of the American Physical SocietyMar 2, 20150 citations

Non-Hermitian spin-orbit-coupling-induced unique dispersion relation and collective dynamics in nonuniform Bose-Einstein condensates

Juncheng Liang, Ai‐Xia Zhang, Ju-Kui Xue

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 ${m}_{2}$ 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 ${m}_{2}>1$ always holds. Negative effective mass can lead to the self-interference effect of condensates, while ${m}_{2}<1$ 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 ${m}_{2}$ , 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 ${m}_{2}<1$ , 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 ${m}_{2}$ . Our results show that the controllable gain-loss engineering in SO-coupled BECs provides a prospect to explore novel quantum many-body physics.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 ${m}_{2}$ 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 ${m}_{2}>1$ always holds. Negative effective mass can lead to the self-interference effect of condensates, while ${m}_{2}<1$ 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 ${m}_{2}$, 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 ${m}_{2}<1$, 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 ${m}_{2}$. Our results show that the controllable gain-loss engineering in SO-coupled BECs provides a prospect to explore novel quantum many-body physics.

Physical Review AMar 12, 20251 citation

Atomic matter of nonzero-momentum Bose-Einstein condensation and orbital current order

W. Vincent Liu, Congjun Wu

The paradigm of Bose-Einstein condensation has been associated with zero momentum to which a macroscopic fraction of bosons condense. Here we propose a new quantum state where bosonic alkali-metal atoms condense at nonzero momenta, defying the paradigm. This becomes possible when the atoms are confined in the $p$ -orbital Bloch band of an optical lattice rather than the usual $s$ -orbital band. The new condensate simultaneously forms an order of transversely staggered orbital currents, reminiscent of orbital antiferromagnetism or $d$ -density wave in correlated electronic systems but different in fundamental ways. We discuss several approaches of preparing atoms to the $p$ -orbital band and propose an ``energy blocking'' mechanism by Feshbach resonance to protect them from decaying to the lowest $s$ -orbital band. Such a model system seems very unique and novel to atomic gases. It suggests a new concept of quantum collective phenomena of no prior example from solid state materials.The paradigm of Bose-Einstein condensation has been associated with zero momentum to which a macroscopic fraction of bosons condense. Here we propose a new quantum state where bosonic alkali-metal atoms condense at nonzero momenta, defying the paradigm. This becomes possible when the atoms are confined in the $p$-orbital Bloch band of an optical lattice rather than the usual $s$-orbital band. The new condensate simultaneously forms an order of transversely staggered orbital currents, reminiscent of orbital antiferromagnetism or $d$-density wave in correlated electronic systems but different in fundamental ways. We discuss several approaches of preparing atoms to the $p$-orbital band and propose an ``energy blocking'' mechanism by Feshbach resonance to protect them from decaying to the lowest $s$-orbital band. Such a model system seems very unique and novel to atomic gases. It suggests a new concept of quantum collective phenomena of no prior example from solid state materials.

arXiv:cond-mat/0601432Physical Review AJul 13, 2006155 citations

{m}_{2}

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

{m}_{2}>1

always holds. Negative effective mass can lead to the self-interference effect of condensates, while

{m}_{2}<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

{m}_{2}

, 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

{m}_{2}<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

{m}_{2}

. Our results show that the controllable gain-loss engineering in SO-coupled BECs provides a prospect to explore novel quantum many-body physics.

p

-orbital Bloch band of an optical lattice rather than the usual

s

-orbital band. The new condensate simultaneously forms an order of transversely staggered orbital currents, reminiscent of orbital antiferromagnetism or

d

-density wave in correlated electronic systems but different in fundamental ways. We discuss several approaches of preparing atoms to the

p

-orbital band and propose an ``energy blocking'' mechanism by Feshbach resonance to protect them from decaying to the lowest

s

-orbital band. Such a model system seems very unique and novel to atomic gases. It suggests a new concept of quantum collective phenomena of no prior example from solid state materials.