Magnetic properties of one-dimensional Fermi gases in an optical cavity

Yan-Lin Feng; Jing-Tao Fan; Gang Chen; Suo-Tang Jia

doi:10.7498/aps.68.20181954

Journals >Acta Physica Sinica >Volume 68 >Issue 4 >Page 043702-1 > Article

Acta Physica Sinica
Vol. 68, Issue 4, 043702-1 (2019)

Magnetic properties of one-dimensional Fermi gases in an optical cavity

Yan-Lin Feng^1,2, Jing-Tao Fan^1,2, Gang Chen^1,2,*, and Suo-Tang Jia^1,2

Author Affiliations

¹State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China

²Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

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DOI: 10.7498/aps.68.20181954 Cite this Article

Yan-Lin Feng, Jing-Tao Fan, Gang Chen, Suo-Tang Jia. Magnetic properties of one-dimensional Fermi gases in an optical cavity[J]. Acta Physica Sinica, 2019, 68(4): 043702-1 Copy Citation Text

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Abstract

In this work we show that the superradiance of the cavity photons can give rise to a magnetic transformation for the atomic system when the quasi one-dimensional Fermi gases are coupled to an optical cavity. This magnetic transformation has a close relationship with the atomic detuning and the filling number. When the interaction between the atoms is neglected, the mean-field approximation may be used in the superradiant phase. In this approximation, we analyze the static spin structure factors of the system with different filling numbers and atomic detuning. Then we characterize the cavity photons-assisted magnetic transformation and obtain the phase diagrams which are dependent on the cavity parameters. Finally, the feasible experimental parameters of our results are also discussed.

Keywords

effective optical lattice magnetic correlation spin structure factor superradiance

\begin{aligned} \hat{H} = & \sum_{σ =↑, ↓} \int d x {\hat{Ψ}}_{σ}^{†} (x) \\ \times [\frac{p_{x}^{2}}{2 m} + (V_{0} + U {\hat{a}}^{†} \hat{a}) \cos^{2} (k_{R} x)] {\hat{Ψ}}_{σ} (x) \\ + η_{A} ({\hat{a}}^{†} + \hat{a}) [\int d x {\hat{Ψ}}_{↑}^{†} (x) \cos (k_{R} x) \\ \times {\hat{Ψ}}_{↓} (x) + H . c .] - Δ_{c} {\hat{a}}^{†} \hat{a}, \end{aligned}

(1)

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$ \hat a = \frac{{{\eta _{\rm{A}}}\left[{\displaystyle\int {{\rm{d}}x} \hat \Psi _ \uparrow ^\dagger \left( x \right)\cos \left( {{k_{\rm{R}}}x} \right){{\hat \Psi }_ \downarrow }\left( x \right) + {\rm{H}}.{\rm{c}}.} \right]}}{{{\Delta _{\rm{c}}} + {\rm{i}}\kappa - U\sum\limits_{\sigma = \uparrow, \downarrow } {\displaystyle\int {{\rm{d}}x\hat \Psi _\sigma ^\dagger \left( x \right)} } {{\hat \Psi }_\sigma }\left( x \right){{\cos }^2}\left( {{k_{\rm{R}}}x} \right)}}. $

(2)

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\begin{aligned} α & = \frac{η_{A} [\int d x ⟨ {\hat{Ψ}}_{↑}^{†} (x) {\hat{Ψ}}_{↓} (x) ⟩ \cos (k_{R} x) + H . c .]}{Δ_{c} + i κ - U \sum_{σ =↑, ↓} \int d x ⟨ {\hat{Ψ}}_{σ}^{†} (x) {\hat{Ψ}}_{σ} (x) ⟩ \cos^{2} (k_{R} x)} \\ N & = \sum_{σ =↑, ↓} \int d x ⟨ {\hat{Ψ}}_{σ}^{†} (x) {\hat{Ψ}}_{σ} (x) ⟩ \end{aligned}

. $

(3)

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${S_z}\left( k \right) = \frac{1}{L}\sum\limits_{l, j} {{{\rm{e}}^{{\rm{i}}k\left( {l - j} \right)}}\left\langle {s_l^zs_j^z} \right\rangle }, $

(4)

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$\hat H \!=\! {t_{\rm{s}}}\!\!\sum\limits_{\left\langle {i, j} \right\rangle, \sigma } {\hat c_{i\sigma }^\dagger } {\hat c_{j\sigma }} \!+\! \sum\limits_{\left\langle {i, j} \right\rangle } {{t_{{\rm{so}}}}\left( {i, j} \right)\left( {\hat c_{i \uparrow }^\dagger {{\hat c}_{j \downarrow }} \!+\! {\rm{H}}.{\rm{c}}.} \right)}\! - {\Delta _{\rm{c}}}{\hat a^\dagger }\hat a, $

(5)

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\begin{aligned} \hat{H} = & \sum_{k} (\begin{array}{c} φ_{k ↑}^{†} φ_{k ↓}^{†} \end{array}) \\ \times (\begin{array}{c} 2 t_{s} \cos (k_{R} a) - 2 i t_{s o} \sin (k_{R} a) \\ 2 i t_{s o} \sin (k_{R} a) - 2 t_{s} \cos (k_{R} a) \end{array}) \\ \times (\begin{array}{c} φ_{k ↑} \\ φ_{k ↓} \end{array}) - Δ_{c} {\hat{a}}^{†} \hat{a}, \end{aligned}

(6)

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$\hat H \!=\! {t_{\rm{s}}}\sum\limits_{\left\langle {i, j} \right\rangle, \sigma }\!{\hat c_{i\sigma }^\dagger } {\hat c_{j\sigma }} \!+\! \sum\limits_i {{t_{{\rm{cd}}}}\left( i \right)\left( {\hat c_{i \uparrow }^\dagger {{\hat c}_{i \downarrow }} \!+\! \hat c_{i \downarrow }^\dagger {{\hat c}_{i \uparrow }}} \right)} - {\Delta _{\rm{c}}}{\hat a^\dagger }\hat a, $

(7)

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\begin{aligned} \hat{H} = & \sum_{k} (\begin{array}{c} φ_{k ↑}^{†} φ_{k ↓}^{†} \end{array}) \\ \times (\begin{array}{c} 2 t_{s} \cos (k_{R} a) t_{c d} \\ t_{c d} - 2 t_{s} \cos (k_{R} a) \end{array}) \\ \times (\begin{array}{c} φ_{k ↑} \\ φ_{k ↓} \end{array}) - Δ_{c} {\hat{a}}^{†} \hat{a} . \end{aligned}

(8)

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Yan-Lin Feng, Jing-Tao Fan, Gang Chen, Suo-Tang Jia. Magnetic properties of one-dimensional Fermi gases in an optical cavity[J]. Acta Physica Sinica, 2019, 68(4): 043702-1

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