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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.
[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 物理学报 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 物理学报 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 物理学报 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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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.
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kF/ER不同的值对应不同的填充, kF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.
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)).
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)).
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)). -
[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 物理学报 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 物理学报 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 物理学报 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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