Zhao Xiu-Qin; Zhang Wen-Hui

doi:10.7498/aps.73.20241103

Abstract

In this paper, the quantum phase transition of cold atoms in a two-mode photomechanical cavity with nonlinear coupling between the optical field (mode 1) and the mechanical oscillator is studied on the basis of the two-mode Dicke model. The functional of the ground state energy of the system is obtained by spin coherent states and variational method. By solving and judging the stability, the phase transformation point and ground state phase diagram are obtained. It is found that there are bistable state of normal phase and reverse normal phase, coexistent state of superradiation phase and reversed normal phase, and reversed normal phase that exists alone. The different interaction strengths between atoms and two-mode light fields greatly affect the value of the phase transition point. There is a quantum phase transition from a normal phase through a phase transition point to a superradiant phase. The light-phonon nonlinear coupling has no effect on the phase transition point, but induces the collapse of the superradiant phase. There is a turning point through which the quantum phase transition from the superradiant phase to the reversed normal phase can be realized. The region of the superradiation phase decreases with the increase of the photon-phonon coupling, and it shrinks to zero at the critical value of the coupling, that is, the turning point and the phase transition point coincide, and there may be a reversal of the atomic population between the two normal phases. The nonlinear coupling of the light-phonon also produces an unstable non-zero photon state, which corresponds to the superradiation state. In the absence of mechanical oscillators, the results of the two-mode Dicke model are returned.

Keywords:

Authors and contacts

Corresponding author: Zhang Wen-Hui, zhangwh@tynu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12304404) and the Basic Research Project of Shanxi Province, China (Grant No. 202203021222236).

FullText HTML : translate this paragraph

References

[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
[45]

Cited By

DownLoad: Full-Size Img PowerPoint

区域	$ \left( {\dfrac{{{g_1}}}{{{\omega _{\text{a}}}}}, \dfrac{{{g_2}}}{{{\omega _{\text{a}}}}}} \right) $	$ (\overline{{\gamma }_{1}^{2}}, \text{ }\overline{{\gamma }_{2}^{2}}) $	$ {\varepsilon _ - } $	$ {{\boldsymbol{H}}_ - } = \left[ {\begin{array}{*{20}{c}} {\dfrac{{{\partial ^2}{\varepsilon _ - }}}{{\partial \gamma _1^2}}}&{\dfrac{{{\partial ^2}{\varepsilon _ - }}}{{\partial {\gamma _1}\partial {\gamma _2}}}} \\ {\dfrac{{{\partial ^2}{\varepsilon _ - }}}{{\partial {\gamma _2}\partial {\gamma _1}}}}&{\dfrac{{{\partial ^2}{\varepsilon _ - }}}{{\partial \gamma _2^2}}} \end{array}} \right] $	特征值$ \left[ {{H_ - }} \right] $
I	(0.3, 0.4)	(0, 0)	–0.5	$ \left[ {\begin{array}{*{20}{c}} {1.82}&{ - 0.24} \\ { - 0.24}&{1.68} \end{array}} \right] $	(2, 1.5)
II	(0.8, 0.7)	(0.0347, 0.0266)	–0.5037	$ \left[ {\begin{array}{*{20}{c}} {1.1129}&{ - 0.7762} \\ { - 0.7762}&{1.3208} \end{array}} \right] $	(2, 0.4337)
III	(0.6, 1.6)	(0.0794, 0.5649)	–0.8156	$ \left[ {\begin{array}{*{20}{c}} {1.9711}&{ - 0.0711} \\ { - 0.0711}&{1.7943} \end{array}} \right] $	(2, 1.7654)
IV	(1.5, 1.5)	(0.5347, 0.5347)	–1.1806	$ \left[ {\begin{array}{*{20}{c}} {1.9506}&{ - 0.0494} \\ { - 0.0494}&{1.9506} \end{array}} \right] $	(2, 1.9012)
V	(1.5, 0.5)	(0.4725, 0.0525)	–0.725	$ \left[ {\begin{array}{*{20}{c}} {1.7119}&{ - 0.0960} \\ { - 0.0960}&{1.9680} \end{array}} \right] $	(2, 1.6800)

DownLoad: CSV

区域	$ \left( {\dfrac{{{g_1}}}{{{\omega _{\text{a}}}}}, \dfrac{{{g_2}}}{{{\omega _{\text{a}}}}}} \right) $	$ (\overline {\gamma _1^2} , {\text{ }}\overline {\gamma _2^2} ) $	$ {\varepsilon _ - } $	$ {{\boldsymbol{H}}_ - } = \left[ \begin{array}{*{20}{c}} {\dfrac{{{\partial ^2}{\varepsilon _ - }}}{{\partial \gamma _1^2}}}&{\dfrac{{{\partial ^2}{\varepsilon _ - }}}{{\partial {\gamma _1}\partial {\gamma _2}}}} \\ {\dfrac{{{\partial ^2}{\varepsilon _ - }}}{{\partial {\gamma _2}\partial {\gamma _1}}}}&{\dfrac{{{\partial ^2}{\varepsilon _ - }}}{{\partial \gamma _2^2}}} \end{array} \right] $	特征值$ \left[ {{H_ - }} \right] $
I	(0.4, 0.3)	(4.5925, 0.01716)	1.2585	$ \left[ \begin{array}{*{20}{c}} { - 3.5436}&{ - 0.0326} \\ { - 0.0326}&{1.9674} \end{array} \right] $	(–3.5438, 1.9676)
II	(0.7, 0.8)	$ \left\{ {\begin{aligned} &{\left( {4.1771, 0.1478} \right)} \\ &{\left( {0.0273, 0.0353} \right)} \end{aligned}} \right. $	$ \left\{ {\begin{aligned} &{0.7714} \\ &{ - 0.5038} \end{aligned}} \right. $	$ \left\{ \begin{aligned} {\left[ \begin{array}{{20}{c}} { - 3.033}&{ - 0.0237} \\ { - 0.0237}&{1.9730} \end{array} \right]} \\ {\left[ \begin{array}{{20}{c}} {1.2929}&{ - 0.7707} \\ { - 0.7707}&{1.1192} \end{array} \right]} \end{aligned} \right. $	$ \left\{ {\begin{aligned} &{\left( { - 0.0334, 1.9731} \right)} \\ &{\left( {1.9816, 0.4305} \right)} \end{aligned}} \right. $
III	(0.8, 1.2)	$ \left\{ {\begin{aligned} &{\left( {4.0258, 0.3439} \right)} \\ &{\left( {0.1303, 0.2781} \right)} \end{aligned}} \right. $	$ \left\{ {\begin{aligned} &{0.3866} \\ & { - 0.6418} \end{aligned}} \right. $	$ \left\{ {\begin{aligned} {\left[ \begin{array}{{20}{c}} { - 2.8431}&{ - 0.0182} \\ { - 0.0182}&{1.9727} \end{array} \right]} \\ {\left[ \begin{array}{{20}{c}} {1.7048}&{ - 0.2082} \\ { - 0.2082}&{1.6878} \end{array} \right]} \end{aligned}} \right. $	$ \left\{ {\begin{aligned} &{\left( { - 2.8432, 1.9728} \right)} \\ &{\left( {1.9046, 1.4880} \right)} \end{aligned}} \right. $
IV	(1.5, 1.5)	$ \left\{ {\begin{aligned} &{\left( {2.7669, 0.5519} \right)} \\ &{\left( {0.7439, 0.5390} \right)} \end{aligned}} \right. $	$ \left\{ {\begin{aligned} &{ - 1.0907} \\ & { - 1.2190} \end{aligned}} \right. $	$ \left\{ {\begin{aligned} {\left[ \begin{array}{{20}{c}} { - 1.3319}&{ - 0.0116} \\ { - 0.0116}&{1.9884} \end{array} \right]} \\ {\left[ \begin{array}{{20}{c}} {1.7048}&{ - 0.2082} \\ { - 0.2082}&{1.6878} \end{array} \right]} \end{aligned}} \right. $	$ \left\{ {\begin{aligned} &{\left( { - 1.3220, 1.9884} \right)} \\ & {\left( {1.9632, 1.0673} \right)} \end{aligned}} \right. $
V	(1.2, 0.8)	$ \left\{ {\begin{aligned} &{\left( {3.4015, 0.1540} \right)} \\ &{\left( {0.3252, 0.1263} \right)} \end{aligned}} \right. $	$ \left\{ {\begin{aligned}& { - 0.1776} \\ &{ - 0.6491} \end{aligned}} \right. $	$ \left\{ {\begin{aligned} &{\left[ \begin{array}{{20}{c}} { - 2.1072}&{ - 0.0141} \\ { - 0.0141}&{1.9907} \end{array} \right]} \\ &{\left[ \begin{array}{{20}{c}} {1.3319}&{ - 0.1853} \\ { - 0.1853}&{1.8765} \end{array} \right]} \end{aligned}} \right. $	$ \left\{ {\begin{aligned} &{\left( { - 2.1073, 1.9907} \right)} \\ &{\left( {1.9336, 1.2748} \right)} \end{aligned}} \right. $

DownLoad: CSV

$ {{{g_1}}}/{{{\omega _{\text{a}}}}} $	$ \overline {\gamma _1^2} $	$ {\varepsilon _ + } $	$ {{{\partial ^2}{\varepsilon _ + }}}/{{\partial \gamma _1^2}} $
0.4	5.0910	3.531	–4.0728
0.8	5.0614	4.3676	–4.0491
1.2	5.0437	5.2408	–4.0350
1.6	5.0336	6.1243	–4.0269

DownLoad: CSV

map

[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
[45]

[1]	Zhao Xiu-Qin, Zhang Wen-Hui, Wang Hong-Mei. Nonlinear interactions caused novel quantum phase transitions in two-mode Dicke models. Acta Physica Sinica, 2024, 73(16): 160302. doi: 10.7498/aps.73.20240665
[2]	Tan Hui, Cao Rui, Li Yong-Qiang. Quantum simulation of ultracold atoms in optical lattice based on dynamical mean-field theory. Acta Physica Sinica, 2023, 72(18): 183701. doi: 10.7498/aps.72.20230701
[3]	Chen Xi-Hao, Xia Ji-Hong, Li Meng-Hui, Zhai Fu-Qiang, Zhu Guang-Yu. Quantum phases and transitions of spin-1/2 quantum compass chain. Acta Physica Sinica, 2022, 71(3): 030302. doi: 10.7498/aps.71.20211433
[4]	You Bing-Ling, Liu Xue-Ying, Cheng Shu-Jie, Wang Chen, Gao Xian-Long. The quantum phase transition in the Jaynes-Cummings lattice model and the Rabi lattice model. Acta Physica Sinica, 2021, 70(10): 100201. doi: 10.7498/aps.70.20202066
[5]	. A study in quantum phases and transitions of spin-1/2 quantum compass chain. Acta Physica Sinica, 2021, (): . doi: 10.7498/aps.70.20211433
[6]	Zhou Xiao-Fan, Fan Jing-Tao, Chen Gang, Jia Suo-Tang. Exotic supersolid phase of one-dimensional Bose-Hubbard model inside an optical cavity. Acta Physica Sinica, 2021, 70(19): 193701. doi: 10.7498/aps.70.20210778
[7]	Bao An. Mott transition of fermions in anisotropic ruby lattice. Acta Physica Sinica, 2021, 70(23): 230305. doi: 10.7498/aps.70.20210963
[8]	Chen Ai-Min, Liu Dong-Chang, Duan Jia, Wang Hong-Lei, Xiang Chun-Huan, Su Yao-Heng. Quantum phase transition and topological order scaling in spin-1 bond-alternating Heisenberg model with Dzyaloshinskii-Moriya interaction. Acta Physica Sinica, 2020, 69(9): 090302. doi: 10.7498/aps.69.20191773
[9]	Liu Biao, Zhou Xiao-Fan, Chen Gang, Jia Suo-Tang. Current phases in Hofstadter ladder with staggered hopping. Acta Physica Sinica, 2020, 69(8): 080501. doi: 10.7498/aps.69.20191964
[10]	Wen Kai, Wang Liang-Wei, Zhou Fang, Chen Liang-Chao, Wang Peng-Jun, Meng Zeng-Ming, Zhang Jing. Experimental realization of Mott insulator of ultracold ⁸⁷Rb atoms in two-dimensional optical lattice. Acta Physica Sinica, 2020, 69(19): 193201. doi: 10.7498/aps.69.20200513
[11]	Xie Wu, Shen Bin, Zhang Yong-Jun, Guo Chun-Yu, Xu Jia-Cheng, Lu Xin, Yuan Hui-Qiu. Heavy fermion materials and physics. Acta Physica Sinica, 2019, 68(17): 177101. doi: 10.7498/aps.68.20190801
[12]	Chen Xi-Hao, Wang Xiu-Juan. Topological orders and quantum phase transitions in a one-dimensional extended quantum compass model. Acta Physica Sinica, 2018, 67(19): 190301. doi: 10.7498/aps.67.20180855
[13]	Huang Shan, Liu Ni, Liang Jiu-Qing. Stimulated radiation characteristics and quantum phase transition for two-component Bose-Einstein condensate in optical cavity. Acta Physica Sinica, 2018, 67(18): 183701. doi: 10.7498/aps.67.20180971
[14]	Song Jia-Li, Zhong Ming, Tong Pei-Qing. Quantum phase transitions of one-dimensional period-two anisotropic XY models in a transverse field. Acta Physica Sinica, 2017, 66(18): 180302. doi: 10.7498/aps.66.180302
[15]	Yu Li-Xian, Liang Qi-Feng, Wang Li-Rong, Zhu Shi-Qun. Firstorder quantum phase transition in the two-mode Dicke model. Acta Physica Sinica, 2014, 63(13): 134204. doi: 10.7498/aps.63.134204
[16]	Liu Ni. Quantum phase transition of a Bose-Einstein condensate in an optical cavity driven by a laser field. Acta Physica Sinica, 2013, 62(1): 013402. doi: 10.7498/aps.62.013402
[17]	Zhao Jian-Hui, Wang Hai-Tao. Quantum phase transition and ground state entanglement of the quantum spin system: a MERA study. Acta Physica Sinica, 2012, 61(21): 210502. doi: 10.7498/aps.61.210502
[18]	Yang Jin-Hu, Wang Hang-Dong, Du Jian-Hua, Zhang Zhu-Jun, Fang Ming-Hu. Ferromagnetic quantum phase transition in Co(S1-xSex)2 system. Acta Physica Sinica, 2009, 58(2): 1195-1199. doi: 10.7498/aps.58.1195
[19]	Yang Jin-Hu, Wang Hang-Dong, Du Jian-Hua, Zhang Zhu-Jun, Fang Ming-Hu. Antiferromagnetic quantum phase transition near x=1.00 in NiS2-xSex system. Acta Physica Sinica, 2008, 57(4): 2409-2414. doi: 10.7498/aps.57.2409
[20]	Shi Zhu-Yi, Tong Hong, Shi Zhu-Ya, Zhang Chun-Mei, Zhao Xing-Zhi, Ni Shao-Yong. A possible route of nuclear quantum phase transition induced by rotation. Acta Physica Sinica, 2007, 56(3): 1329-1333. doi: 10.7498/aps.56.1329

Catalog

Vol. 73, Issue 24 - 2024-12-20

Metrics

Abstract views: 312
PDF Downloads: 15
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板

Abstract

Authors and contacts

Corresponding author: Zhang Wen-Hui, zhangwh@tynu.edu.cn

FullText HTML : translate this paragraph

References

Cited By

Catalog

Metrics

Authors

Referees

About Journal

About

Search

Article

留言板

Abstract

Authors and contacts

Corresponding author: Zhang Wen-Hui, zhangwh@tynu.edu.cn

FullText HTML : translate this paragraph

References

Cited By

Catalog

Metrics

Publishing process

Authors

Referees

About Journal

About