光学微腔中一维费米气的磁性关联特性

冯彦林; 樊景涛; 陈刚; 贾锁堂

doi:10.7498/aps.68.20181954

摘要

对于准一维两组分费米气与光学微腔耦合的系统, 证明了微腔光子的超辐射可以驱动原子系统的磁性转变, 该磁性转变与原子的失谐以及费米子的填充数密切相关. 对于无相互作用原子气, 在超辐射相区内平均场近似合理. 基于该近似, 分析了不同的填充和失谐情况下体系的静态自旋结构因子, 由此刻画出腔光子协助的磁性关联转变, 并得到了依赖于微腔参数的相图. 最后, 对可行的实验参数做了相关讨论.

关键词:

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:

作者及机构信息

1.
山西大学激光光谱研究所, 量子光学与光量子器件国家重点实验室, 太原　030006

2.
山西大学极端光学协同创新中心, 太原　030006

通信作者: 陈刚, chengang971@163.com

基金项目: 国家重点研发计划(批准号: 2017YFA0304203)、国家自然科学基金(批准号: 11674200, 11804204)、教育部长江学者和创新团队发展计划(批准号: IRT13076)和山西省“1331工程”重点学科建设计划资助的课题.

Authors and contacts

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

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

Corresponding author: Chen Gang, chengang971@163.com

Funds: Project supported by the National Key R&D Program of China (Grant No. 2017YFA0304203), the National Natural Science Foundation of China (Grant Nos. 11674200, 11804204), the Program for Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China (Grant No. IRT13076), and the Fund for Shanxi “1331 Project” Key Subjects Construction, China.

文章全文 : translate this paragraph

参考文献

[1]	Bloch I, Dalibard J, Zwerger W 2008 Rev. Mod. Phys. 80 885 Google Scholar
[2]	Ritsch H, Demokos P, Brennecke F, Esslinger T 2013 Rev. Mod. Phys. 85 553 Google Scholar
[3]	Baumann K, Guerlin C, Brennecke F, Esslinger T 2010 Nature (London) 464 1301 Google Scholar
[4]	Landig R, Hruby L, Dogra N, Landini M, Mottl R, Donner T, Esslinger T 2016 Nature (London) 532 476 Google Scholar
[5]	Hruby L, Dogra N, Landini M, Donner T, Esslinger T 2018 PNAS 115 3279 Google Scholar
[6]	Lénard J, Morales A, Zupancic P, Esslinger T, Donner T 2017 Nature (London) 543 87 Google Scholar
[7]	Lénard J, Morales A, Zupancic P, Donner T, Esslinger T 2017 Science 358 1415 Google Scholar
[8]	Caballero-Benitez S F, Mekhov I B 2015 Phys. Rev. Lett. 115 243604 Google Scholar
[9]	Dogra N, Brennecke F, Huber S D, Donner T 2016 Phys. Rev. A 94 023632 Google Scholar
[10]	Chen Y, Yu Z, Zhai H 2016 Phys. Rev. A 93 041601(R)Google Scholar
[11]	Pan J S, Liu X J, Zhang W, Yi W, Guo G C 2015 Phys. Rev. Lett. 115 045303 Google Scholar
[12]	Luo X W, Zhang C 2018 Phys. Rev. Lett. 120 263202 Google Scholar
[13]	谷红明, 黄永清, 王欢欢, 武刚, 段晓峰, 刘凯, 任晓敏 2018 67 144201 Google Scholar Gu H M, Huang Y Q, Wang H H, Wu G, Duan X F, Liu K, Ren X M 2018 Acta Phys. Sin. 67 144201 Google Scholar
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[16]	Cheuk L W, Nichols M A, Lawrence K R, Okan M, Zhang H, Khatami E, Trivedi N, Paiva T, Rigol M, Zwierlein M W 2016 Science 353 1260 Google Scholar
[17]	Hilker T A, Salomon G, Grusdt F, Omran A, Boll M, Demler E, Bloch I, Gross C 2017 Science 357 484 Google Scholar
[18]	Salomon G, Koepsell J, Vijayan J, Hilker T A, Nespolo J, Pollet L, Bloch I, Gross C 2019 Nature 565 56
[19]	Mazurenko A, Chiu C S, Ji G, Parsons M F, Kanasz-Nagy M, Schmidt R, Grusdt F, Demler E, Greif D, Greiner M 2017 Nature 545 462 Google Scholar
[20]	徐志君, 刘夏吟 2011 60 120305 Google Scholar Xu Z J, Liu X Y 2011 Acta Phys. Sin. 60 120305 Google Scholar
[21]	秦帅锋, 郑公平, 马骁, 李海燕, 童晶晶, 杨博 2013 62 110304 Google Scholar Qin S F, Zheng G P, Ma X, Li H Y, Tong J J, Yang B 2013 Acta Phys. Sin. 62 110304 Google Scholar
[22]	Sun N, Zhang P F, Zhai H 2018 arXiv: 1808 03966v1 [cond-mat.quant-gas]
[23]	Fan J T, Zhou X F, Zheng W, Yi W, Chen G, Jia S T 2018 Phys. Rev. A 98 043613 Google Scholar
[24]	Giuliani G, Vignale G 2005 Quantum Theory of the Electron Liquid (Cambridge: Cambridge University Press) pp29-36
[25]	Su W P, Schrieffer J R, Heeger A J 1979 Phys. Rev. Lett. 42 1698 Google Scholar
[26]	Peierls R E 1955 Quantum Theory of Solids (Oxford: Clarendon Press) p108
[27]	Ogata M, Shiba H 1990 Phys. Rev. B 41 2326 Google Scholar
[28]	Costa N C, Mendes-Santos T, Paiva T, Santos R R dos, Scalettar R T 2016 Phys. Rev. B 94 155107 Google Scholar
[29]	Chang C-C, Zhang S 2008 Phys. Rev. B 78 165101 Google Scholar
[30]	Hart R A, Duarte P M, Yang T L, Liu X, Paiva T, Khatami E, Scalettar R T, Trivedi N, Huse D A, Hulet R G 2015 Nature (London) 519 211 Google Scholar
[31]	Liu X-J, Law K T, Ng T K 2014 Phys. Rev. Lett. 112 086401 Google Scholar
[32]	Klinder J, Keβler H, Wolke M, Mathey L, Hemmerich A 2015 PNAS 112 3290 Google Scholar
[33]	Landig R, Brennecke F, Mottl R, Donner T, Esslinger T 2015 Nat. Commun. 6 7046 Google Scholar

施引文献

图 1 (a)超冷费米气沿着腔轴$\hat x$方向被俘获在准一维背景光学晶格中, 费米气被两束圆偏振的横向(沿着$\hat z$方向)抽运激光驱动, 腔模由一束线偏振的纵向(沿着$\hat x$方向)驱动光驱动; (b)费米子的能级跃迁图, 图中相关的跃迁过程和符号的定义见正文

Fig. 1. (a) The ultracold fermions are trapped in a quasi-one-dimensional background optical lattice along the cavity axis $\hat x$. These fermions are pumped by two circular-polarized transverse (along $\hat z$) lasers and the cavity mode is driven by a linear-polarized longitudinal (along $\hat x$) laser. (b) the atomic energy levels and their transition. See main text for the corresponding transition processes and the definition of the labels.

下载: 全尺寸图片幻灯片

图 2 a)蓝失谐的情况$\Delta > 0$, 光场$\left| \alpha \right|$在不同的晶格填充下随耦合强度$\eta_ {\rm{A}}$的变化. 图中其他参数的选择: ${V_0} = 5{E_{\rm{R}}}$, $\kappa = 100{E_{\rm{R}}}$, ${\Delta _{\rm{c}}} = - 10{E_{\rm{R}}}$, ${k_{\rm{B}}}T = {E_{\rm{R}}}/200$和$U = 5{E_{\rm{R}}}$; (b)红失谐的情况$\Delta < 0$, 光场$\left| \alpha \right|$在不同的晶格填充下随耦合强度$\eta_ {\rm{A}}$的变化. 图中其它参数的选择: ${V_0} = - 5{E_{\rm{R}}}$, $\kappa = 100{E_{\rm{R}}}$, ${\Delta _{\rm{c}}} = - 100{E_{\rm{R}}}$, ${k_{\rm{B}}}T = {E_{\rm{R}}}/200$和$U = - {E_{\rm{R}}}$. 我们考虑的具有80个格点的晶格对应不同的填充, 其中k_F/E_R不同的值对应不同的填充, k_F为费米动量

Fig. 2. (a) The cavity field $\left| \alpha \right|$ for systems in different fillings with $\Delta > 0$. The plotted parameters are chosen as ${V_0} = 5{E_{\rm{R}}}$, $\kappa = 100{E_{\rm{R}}}$, ${\Delta _{\rm{c}}} = - 10{E_{\rm{R}}}$, ${k_{\rm{B}}}T = {E_{\rm{R}}}/200$, and $U = 5{E_{\rm{R}}}$. (b) the cavity field $\left| \alpha \right|$ for systems in different fillings with $\Delta < 0$. The plotted parameters are chosen as ${V_0} = - 5{E_{\rm{R}}}$, $\kappa = 100{E_{\rm{R}}}$, ${\Delta _{\rm{c}}} = - 100{E_{\rm{R}}}$, ${k_{\rm{B}}}T = {E_{\rm{R}}}/200$, and $U = - {E_{\rm{R}}}$. We consider a lattice of sites 80 with different fillings.

下载: 全尺寸图片幻灯片

图 3 静态自旋结构因子${S_z}\left( k \right)$　(a) ${k_{\rm{F}}}/{E_{\rm{R}}}=3/8$; (b) ${k_{\rm{F}}}/{E_{\rm{R}}}=1/2$; (c) ${k_{\rm{F}}}/{E_{\rm{R}}}=5/8$. (图中对应的其它参数的选择与图2(a)中一致)

Fig. 3. The spin structure factors ${S_z}\left( k \right)$ for systems in different fillings: (a) ${k_{\rm{F}}}/{E_{\rm{R}}}=3/8$; (b) ${k_{\rm{F}}}/{E_{\rm{R}}}=1/2$; (c) ${k_{\rm{F}}}/{E_{\rm{R}}}=5/8$ (The plotted parameters are the same as those in Fig. 2(a)).

下载: 全尺寸图片幻灯片

图 4 静态自旋结构因子${S_z}\left( k \right)$　(a) ${k_{\rm{F}}}/{E_{\rm{R}}}=3/8$; (b) ${k_{\rm{F}}}/{E_{\rm{R}}}=1/2$; (c) ${k_{\rm{F}}}/{E_{\rm{R}}}=5/8$(图中对应的其他参数的选择与图2(b)中一致)

Fig. 4. The spin structure factors ${S_z}\left( k \right)$ for systems in different fillings: (a) ${k_{\rm{F}}}/{E_{\rm{R}}}=3/8$; (b) ${k_{\rm{F}}}/{E_{\rm{R}}}=1/2$; (c) ${k_{\rm{F}}}/{E_{\rm{R}}}=5/8$ (The plotted parameters are the same as those in Fig. 2(b)).

下载: 全尺寸图片幻灯片

图 5 (a)蓝失谐时${k_{\rm{F}}} - {\eta _{\rm{A}}}$平面上的相图(M, AF-SR和FM-SR分别代表金属相、反铁磁关联的超辐射相和铁磁关联的超辐射相, 其它参数的选择与图2(a)相同); (b)红失谐时${k_{\rm{F}}} - {\eta _A}$平面上的相图(AF-SR代表反铁磁关联的超辐射相, 对应的其他参数的选择与图2(b)中一致)

Fig. 5. (a) The phase diagram in the ${k_{\rm{F}}} - {\eta _A}$ plane for the system with blue-detuned atomic detuning (M, AF-SR, and FM-SR correspond to metallic phase, antiferromagnetic superradiant phase, and ferromagnetic superradiant phase, respectively. The plotted parameters are the same as those in Fig. 2(a)); (b) the phase diagram in the ${k_{\rm{F}}} - {\eta _{\rm{A}}}$ plane for the system with red-detuned atomic detuning (AF-SR corresponds to the antiferromagnetic superradiant phase. The plotted parameters are the same as those in Fig. 2(b)).

下载: 全尺寸图片幻灯片

map

[1]	Bloch I, Dalibard J, Zwerger W 2008 Rev. Mod. Phys. 80 885 Google Scholar
[2]	Ritsch H, Demokos P, Brennecke F, Esslinger T 2013 Rev. Mod. Phys. 85 553 Google Scholar
[3]	Baumann K, Guerlin C, Brennecke F, Esslinger T 2010 Nature (London) 464 1301 Google Scholar
[4]	Landig R, Hruby L, Dogra N, Landini M, Mottl R, Donner T, Esslinger T 2016 Nature (London) 532 476 Google Scholar
[5]	Hruby L, Dogra N, Landini M, Donner T, Esslinger T 2018 PNAS 115 3279 Google Scholar
[6]	Lénard J, Morales A, Zupancic P, Esslinger T, Donner T 2017 Nature (London) 543 87 Google Scholar
[7]	Lénard J, Morales A, Zupancic P, Donner T, Esslinger T 2017 Science 358 1415 Google Scholar
[8]	Caballero-Benitez S F, Mekhov I B 2015 Phys. Rev. Lett. 115 243604 Google Scholar
[9]	Dogra N, Brennecke F, Huber S D, Donner T 2016 Phys. Rev. A 94 023632 Google Scholar
[10]	Chen Y, Yu Z, Zhai H 2016 Phys. Rev. A 93 041601(R)Google Scholar
[11]	Pan J S, Liu X J, Zhang W, Yi W, Guo G C 2015 Phys. Rev. Lett. 115 045303 Google Scholar
[12]	Luo X W, Zhang C 2018 Phys. Rev. Lett. 120 263202 Google Scholar
[13]	谷红明, 黄永清, 王欢欢, 武刚, 段晓峰, 刘凯, 任晓敏 2018 67 144201 Google Scholar Gu H M, Huang Y Q, Wang H H, Wu G, Duan X F, Liu K, Ren X M 2018 Acta Phys. Sin. 67 144201 Google Scholar
[14]	Parsons M F, Mazurenko A, Chiu C S, Ji G, Greif D, Greiner M 2016 Science 353 1253 Google Scholar
[15]	Boll M, Hilker T A, Salomon G, Omran A, Nespolo J, Pollet L, Bloch I, Gross C 2016 Science 353 1257 Google Scholar
[16]	Cheuk L W, Nichols M A, Lawrence K R, Okan M, Zhang H, Khatami E, Trivedi N, Paiva T, Rigol M, Zwierlein M W 2016 Science 353 1260 Google Scholar
[17]	Hilker T A, Salomon G, Grusdt F, Omran A, Boll M, Demler E, Bloch I, Gross C 2017 Science 357 484 Google Scholar
[18]	Salomon G, Koepsell J, Vijayan J, Hilker T A, Nespolo J, Pollet L, Bloch I, Gross C 2019 Nature 565 56
[19]	Mazurenko A, Chiu C S, Ji G, Parsons M F, Kanasz-Nagy M, Schmidt R, Grusdt F, Demler E, Greif D, Greiner M 2017 Nature 545 462 Google Scholar
[20]	徐志君, 刘夏吟 2011 60 120305 Google Scholar Xu Z J, Liu X Y 2011 Acta Phys. Sin. 60 120305 Google Scholar
[21]	秦帅锋, 郑公平, 马骁, 李海燕, 童晶晶, 杨博 2013 62 110304 Google Scholar Qin S F, Zheng G P, Ma X, Li H Y, Tong J J, Yang B 2013 Acta Phys. Sin. 62 110304 Google Scholar
[22]	Sun N, Zhang P F, Zhai H 2018 arXiv: 1808 03966v1 [cond-mat.quant-gas]
[23]	Fan J T, Zhou X F, Zheng W, Yi W, Chen G, Jia S T 2018 Phys. Rev. A 98 043613 Google Scholar
[24]	Giuliani G, Vignale G 2005 Quantum Theory of the Electron Liquid (Cambridge: Cambridge University Press) pp29-36
[25]	Su W P, Schrieffer J R, Heeger A J 1979 Phys. Rev. Lett. 42 1698 Google Scholar
[26]	Peierls R E 1955 Quantum Theory of Solids (Oxford: Clarendon Press) p108
[27]	Ogata M, Shiba H 1990 Phys. Rev. B 41 2326 Google Scholar
[28]	Costa N C, Mendes-Santos T, Paiva T, Santos R R dos, Scalettar R T 2016 Phys. Rev. B 94 155107 Google Scholar
[29]	Chang C-C, Zhang S 2008 Phys. Rev. B 78 165101 Google Scholar
[30]	Hart R A, Duarte P M, Yang T L, Liu X, Paiva T, Khatami E, Scalettar R T, Trivedi N, Huse D A, Hulet R G 2015 Nature (London) 519 211 Google Scholar
[31]	Liu X-J, Law K T, Ng T K 2014 Phys. Rev. Lett. 112 086401 Google Scholar
[32]	Klinder J, Keβler H, Wolke M, Mathey L, Hemmerich A 2015 PNAS 112 3290 Google Scholar
[33]	Landig R, Brennecke F, Mottl R, Donner T, Esslinger T 2015 Nat. Commun. 6 7046 Google Scholar

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光学微腔中一维费米气的磁性关联特性