王林雪，郭慧，劉濤，張曉斐

基于光晶格鐘的自旋軌道耦合簡介

王林雪1,2,3，郭慧1,2,3，劉濤1,2,3，張曉斐1,2,3

（1.中國科學(xué)院 國家授時(shí)中心，西安 710600；2.中國科學(xué)院 時(shí)間頻率基準(zhǔn)重點(diǎn)實(shí)驗(yàn)室，西安 710600；3. 中國科學(xué)院大學(xué) 天文與空間科學(xué)學(xué)院，北京 101048）

基于光晶格原子鐘實(shí)現(xiàn)人造自旋軌道耦合的相關(guān)研究進(jìn)展，簡要說明利用光晶格原子鐘實(shí)現(xiàn)自旋軌道耦合的基本原理。通過與傳統(tǒng)實(shí)現(xiàn)自旋軌道耦合的拉曼耦合方案相比較，指出利用光晶格原子鐘實(shí)現(xiàn)自旋軌道耦合方案的優(yōu)越性。討論了自旋軌道耦合光晶格原子鐘在量子簡并區(qū)域可能實(shí)現(xiàn)的奇異物態(tài)和新奇量子現(xiàn)象。強(qiáng)調(diào)了光鐘平臺在超冷原子新物態(tài)的制備、操控和測量等方面扮演的重要角色。

光晶格原子鐘；自旋軌道耦合；超冷原子氣體；新奇量子態(tài)

0 引言

光鐘是以光學(xué)波段的量子躍遷作為頻率標(biāo)準(zhǔn)的高精度時(shí)間測量工具[1]。光晶格原子鐘[2-3]作為光鐘的一種，其頻率穩(wěn)定度和不確定度已達(dá)到10-19量級[4]，是目前性能指標(biāo)最高的原子鐘，有望替代銫原子噴泉鐘成為新一代秒定義的基準(zhǔn)鐘[5-6]。

光鐘不但提供高精度的時(shí)間頻率信號，而且光鐘系統(tǒng)本身也是一個(gè)人類測量精度極高的科學(xué)與技術(shù)研究平臺，在高精度測量和基礎(chǔ)物理學(xué)方面有重要應(yīng)用?？捎糜诰軠y量光學(xué)躍遷的同位素頻移[7]進(jìn)而檢驗(yàn)標(biāo)準(zhǔn)模型的正確性，探測超越標(biāo)準(zhǔn)模型的新粒子和相互作用[8]；可用于萬有引力常數(shù)、精細(xì)結(jié)構(gòu)常數(shù)、質(zhì)子電子質(zhì)量比等基本物理常數(shù)的測定[9-11]；還可用于驗(yàn)證洛倫茲協(xié)變[12-13]和探測暗物質(zhì)[14]等。隨著光鐘技術(shù)的不斷發(fā)展，光晶格原子鐘的應(yīng)用范圍已經(jīng)不限于測量領(lǐng)域，還可以用于設(shè)計(jì)和操控新的量子系統(tǒng)，成為超冷原子量子模擬的新工具。

近年來，超冷原子物理的研究加深了人們對物質(zhì)結(jié)構(gòu)、光與物質(zhì)相互作用和基本物理規(guī)律的認(rèn)識[15]。超冷原子物理研究之所以能取得重大成功，依賴于其在幾個(gè)方面的實(shí)驗(yàn)突破，主要包括通過Feshbach共振技術(shù)調(diào)節(jié)原子間的相互作用[16-17]、通過光晶格技術(shù)實(shí)現(xiàn)各種凝聚態(tài)物理模型[18-20]、利用人造自旋軌道耦合實(shí)現(xiàn)各種奇異拓?fù)淞孔討B(tài)[21-25]。

人造自旋軌道耦合是利用激光[26-29]、磁場脈沖[30-32]等手段，將原子的內(nèi)部自旋態(tài)和其外部軌道運(yùn)動(dòng)耦合起來。超冷原子自旋軌道耦合的實(shí)驗(yàn)實(shí)現(xiàn)[26-29, 32-34]，一方面突破了凝聚態(tài)系統(tǒng)內(nèi)中性原子無法模擬帶電粒子在電磁場中的響應(yīng)這一瓶頸，拓展了超冷量子氣體作為量子模擬平臺的適用范圍；另一方面為實(shí)現(xiàn)一系列前所未有的全新物理模型提供了可能，為發(fā)現(xiàn)新物態(tài)和探索奇異量子現(xiàn)象開辟了道路。

然而，隨著自旋軌道耦合物理研究的不斷深入，新的自旋軌道耦合形式的實(shí)驗(yàn)實(shí)現(xiàn)面臨一些困難和挑戰(zhàn)。通常自旋軌道耦合的實(shí)驗(yàn)方案，是在超冷堿金屬原子氣體中，通過雙光子拉曼過程將原子的2個(gè)或3個(gè)超精細(xì)能級和高激發(fā)態(tài)耦合實(shí)現(xiàn)的[26-29, 35]。該方案中拉曼激光的單光子失諧受限于激發(fā)態(tài)能級的精細(xì)結(jié)構(gòu)劈裂[35]。由于堿金屬原子激發(fā)態(tài)精細(xì)結(jié)構(gòu)能級劈裂較小，使得系統(tǒng)不可避免地遭受了自發(fā)輻射引起的加熱效應(yīng)。

自發(fā)輻射引起的加熱效應(yīng)的存在，一方面使得系統(tǒng)的壽命比較短，因而當(dāng)前有關(guān)超冷原子自旋軌道耦合的實(shí)驗(yàn)研究大都局限于單粒子、平均場水平，限制了在超越平均場水平上、更長時(shí)間尺度上對系統(tǒng)量子多體動(dòng)力學(xué)性質(zhì)的研究；另一方面對于復(fù)雜的自旋軌道耦合形式，如二維和三維自旋軌道耦合[36-38]、具有SU（3）對稱的自旋軌道耦合[39]等，由于需要引入更多的激光，相關(guān)實(shí)驗(yàn)面臨嚴(yán)峻的挑戰(zhàn)。目前幾乎所有自旋軌道耦合的實(shí)驗(yàn)大都局限在一維情況，只有少數(shù)幾個(gè)實(shí)驗(yàn)實(shí)現(xiàn)了二維形式的自旋軌道耦合[33-34]。

如何有效避免自發(fā)輻射引起的加熱效應(yīng)，是當(dāng)前超冷原子自旋軌道耦合物理研究的重要問題。最近美國國家標(biāo)準(zhǔn)和技術(shù)研究院葉軍研究組等從理論上提出、并在實(shí)驗(yàn)上實(shí)現(xiàn)了基于光晶格原子鐘的人造自旋軌道耦合[40-44]。為突破超冷原子物理自旋軌道耦合研究的瓶頸開辟了新的道路。本文將基于最近的理論和實(shí)驗(yàn)進(jìn)展，簡要說明利用光晶格原子鐘實(shí)現(xiàn)自旋軌道耦合的基本原理，介紹光鐘在超冷原子新物態(tài)的制備、操控和測量等方面扮演的重要角色，并討論其在超冷原子前沿科學(xué)研究領(lǐng)域可能的應(yīng)用。

1 基于光晶格原子鐘實(shí)現(xiàn)自旋軌道耦合的基本原理

在傳統(tǒng)的超冷堿金屬原子氣體中實(shí)現(xiàn)自旋軌道耦合的方案中，由于受到加熱效應(yīng)的影響，使系統(tǒng)的壽命比較短，限制了自旋軌道耦合相關(guān)研究的發(fā)展。隨后，對于激發(fā)態(tài)精細(xì)結(jié)構(gòu)劈裂較大的堿土金屬相關(guān)研究便引起了大家的注意，并且隨著光晶格原子鐘的不斷發(fā)展，給研究自選軌道耦合帶來了新的研究方向。

1.1 基于光晶格原子鐘實(shí)現(xiàn)一維自旋軌道耦合

為了有效抑制自發(fā)輻射引起的加熱效應(yīng)，科學(xué)家提出可以選擇激發(fā)態(tài)精細(xì)結(jié)構(gòu)劈裂較大或激發(fā)態(tài)壽命較長的堿土類金屬原子[24, 40, 45-47]。2016年，葉軍研究組從理論上指出可以在光晶格原子鐘的鐘態(tài)上，利用鐘探測激光的Rabi躍遷實(shí)現(xiàn)自旋軌道耦合。下面我們對相關(guān)的基本原理作簡要介紹。

圖1 基于光晶格鐘實(shí)現(xiàn)自旋軌道耦合的原理圖

1.2 基于光晶格原子鐘實(shí)現(xiàn)高維自旋軌道耦合

圖2 基于光晶格鐘實(shí)現(xiàn)二維自旋軌道耦合的鐘探測激光幾何結(jié)構(gòu)示意圖

1.3 基于光晶格原子鐘實(shí)現(xiàn)自旋軌道耦合的優(yōu)越性

跟拉曼激光耦合方案相比，利用光晶格原子鐘實(shí)現(xiàn)自旋軌道耦合的優(yōu)越性主要表現(xiàn)在以下幾個(gè)方面。① 有效避免了自發(fā)輻射引起的加熱效應(yīng)，相比于堿金屬原子，類堿土金屬原子的激發(fā)態(tài)精細(xì)結(jié)構(gòu)能級劈裂值較大，能有效地避免失諧帶來的加熱效應(yīng)[35]。② 所用的激光頻率更為單一，僅需要用到魔術(shù)波長激光和鐘探測激光兩個(gè)頻率的激光。更少的激光束可以最大限度地避免干涉引起的不穩(wěn)定性[42]。③ 光鐘系統(tǒng)為研究自旋軌道耦合的物理性質(zhì)提供了先進(jìn)的精密測量手段。例如可通過Rabi和Ramsey譜線[40, 44]實(shí)現(xiàn)對原子自旋動(dòng)力學(xué)實(shí)時(shí)、無破壞性的測量。

2 量子簡并區(qū)域的自旋軌道耦合效應(yīng)

光晶格原子鐘的實(shí)驗(yàn)研究已經(jīng)進(jìn)入到量子簡并區(qū)域[55]。費(fèi)米簡并三維光鐘[55]的實(shí)驗(yàn)實(shí)現(xiàn)一方面有利于光鐘性能的進(jìn)一步提高，另一方面也為實(shí)現(xiàn)更高維度[36-38, 41]和更高對稱性的自旋軌道耦合形式[39]開辟了道路。當(dāng)光晶格原子鐘在量子簡并區(qū)域運(yùn)行時(shí)，Rabi和Ramsey光譜法的觀測和操控的靈敏度和適用性將會明顯提高?；诠忡姷母呔裙庾V測量技術(shù)和最近超冷原子系統(tǒng)中發(fā)展的高空間分辨率的投影技術(shù)[56-58]以及磁感相位比對技術(shù)[59-60]，為發(fā)現(xiàn)和觀測新的奇異量子態(tài)和奇異量子現(xiàn)象提供了有力的實(shí)驗(yàn)技術(shù)支持。

通過調(diào)節(jié)鐘探測激光的偏振，可以實(shí)現(xiàn)不同超精細(xì)能級之間的耦合[42]，進(jìn)而可以實(shí)現(xiàn)多維的人造晶格[61]。此時(shí)自旋軌道耦合等效于人造維度上的有效相干隧穿。通過軌道Feshbach技術(shù)[62-64]可調(diào)節(jié)鐘態(tài)上軌道間的自旋交換相互作用，進(jìn)而可以實(shí)現(xiàn)各種類型的量子多體自旋模型。這使我們可以基于光晶格原子鐘研究各種低溫量子磁性[65]、強(qiáng)關(guān)聯(lián)量子態(tài)[66]、拓?fù)涑鲬B(tài)[67]、Weyl半金屬態(tài)[41]、手性邊緣態(tài)[42-43]以及BEC-BCS渡越區(qū)域的新奇量子效應(yīng)等。

基于光晶格原子鐘可研究具有SU（）對稱的碰撞相互作用[68]的超冷原子系統(tǒng)的性質(zhì)。與此同時(shí)，如何借助光鐘系統(tǒng)實(shí)現(xiàn)具有SU（）對稱的自旋軌道耦合是一個(gè)有趣的科學(xué)問題。最近 Ketterle 研究組在SU（2）自旋軌道耦合系統(tǒng)中實(shí)驗(yàn)觀測到具有超固性質(zhì)的條紋相[69-71]，標(biāo)志著超固現(xiàn)象研究的突破性進(jìn)展。然而Ketterle等觀察到的條紋相只在一個(gè)方向上破缺了系統(tǒng)的平移對稱性。我們先前的工作[72]已經(jīng)指出，SU（3）自旋軌道耦合引起的三阱色散關(guān)系，可產(chǎn)生在二維動(dòng)量空間三點(diǎn)凝聚的二維晶格相。不同于Ketterle觀察到的條紋相，該晶格相在兩個(gè)方向上同時(shí)破缺了系統(tǒng)的平移對稱性。下一步，我們將研究如何借助光鐘的優(yōu)勢平臺設(shè)計(jì)合適的自旋軌道耦合形式，進(jìn)而實(shí)現(xiàn)在三個(gè)方向上同時(shí)破缺系統(tǒng)平移對稱性的超固相。

3 結(jié)語

本文簡述了基于光晶格原子鐘實(shí)現(xiàn)自旋軌道耦合的實(shí)驗(yàn)方案，并討論了光晶格原子鐘在量子簡并區(qū)域可能實(shí)現(xiàn)的各種奇異物態(tài)和奇異量子現(xiàn)象。光鐘技術(shù)的不斷發(fā)展進(jìn)步，為超冷量子氣體研究提供了新的實(shí)驗(yàn)研究平臺和高超的精密測量手段。而對于超冷量子系統(tǒng)物理性質(zhì)的研究，如何反過來推動(dòng)光鐘技術(shù)的發(fā)展進(jìn)步，是一個(gè)重要的開放性課題。

[1] LUDLOW A D, BOYD M M, YE J, et al. Optical atomic clocks[J]. Reviews of Modern Physics, 2015, 87(2): 637-701.

[2] KATORI H. Optical-lattice clock sets new standard for timekeeping[J]. Physics Today, 2014, 67(3): 2294-2296.

[3] DEREVIANKO A, KATORI H. Colloquium: physics of optical lattice clocks[J]. Reviews of Modern Physics, 2011(83): 331.

[4] GREW W M, ZHANG X, FASANO R J, et al. Atomic clock performance enabling geodesy below the centimeter level[J]. Nature, 2018(564): 87-90.

[5] GREBING C, AI-MASOUDI A, DORSCHER S, et al. Realization of a timescale with an accurate optical clock[J]. Optica, 2015(3): 563.

[6] HACHISU H, NAKAGAWA F, HANADO Y, et al. Months-long real-time generation of a time scale based on an optical clock[J]. Scientific Reports, 2018, 8(1): 4243-4247.

[7] TAKANO T, MIZUSHIMA R, KATORI H. Precise determination of the isotope shift of Sr-88-Sr-87 optical lattice clock by sharing perturbations[J]. Applied Physics Express, 2017, 10(7): 2801.

[8] DELAUNAY C, OZERI R, PEREZ G, et al. Probing atomic higgs-like forces at the precision frontier[J]. Physical Review D, 2017, 96(9): 3001.

[9] ROSENBAND T, HUME D B, SCHMIDT P O, et al. Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place[J]. Science, 2008, 319(5871): 1808-1819.

[10] GODUN R M, NISBET-JONES P B R, JONES J M, et al. Frequency ratio of two optical clock tranditions in171Yb+and constraints on the time variation of fundamental[J]. Physical Review Letters, 2014, 113(21): 801.

[11] HUNTEMANN N, LIPPHARDT B, TAMM C, et al. Improved limit on a temporal variation ofm/mfrom comparisons of Yb+and Cs atomic clocks[J]. Physical Review Letters, 2014, 113(21): 802.

[12] TOBAR M E, STANWIX P L, MCFERRAN J J M, et al. Testing local position and fundamental constant invariance due to periodic gravitational and boost using long-term comparision of the SYRTE atomic fountains and H-masers[J]. Physical Review D, 2013, 87(12): 2004.

[13] DELVA P, LODEWYCK J, BILICKI S, et al. Test of special relativity using a fiber network of optical clocks[J]. Physical Review Letters, 2017, 118(22): 1102.

[14] DEREVIANKO A, POSPELOV M. Hunting for topological dark matter with atomic clocks[J]. Nature Physics, 2014(10): 933-936.

[15] YE J. Preface: special topic on cold atoms[J]. National Science Review,2016(3): 165.

[16] GRIMN R, JULIENNE P. Feshbach resonances in ultracold gases[J]. Reviews of Modern Physics, 2010(82): 1225.

[17] K?HLER T, GóRAL K. Production of cold molecules via magnetically tunable Feshbach resonances[J]. Reviews of Modern Physics, 2006(78): 1311.

[18] BLOCH I. Many-body physics with ultracold gases[J]. Reviews of Modern Physics, 2008(80): 885.

[19] MORSCH O. Dynamics of Bose-Einstein condensates in optical lattices[J]. Reviews of Modern Physics, 2006(78): 179.

[20] LEWENSTEIN M, SANPERA A, AHUFINGER V, et al. Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond[J]. Advances in Physics, 2007, 56(2): 243-379.

[21] GALITSKI V, SPIELMAN I B. Spin-orbit coupling in quantum gases[J]. Nature, 2013(49): 49-54.

[22] MANCHON A, KOO H C, NITTA J, et al. New perspectives for Rashba spin-orbit coupling[J]. Nature Materials, 2015, 14(9): 871-882.

[23] GOLDMAN N, JUZELIUNAS G, OHBERG P, et al. Light-induced gauge fields for ultracold atoms[J]. Reports on Progress in Physics, 2014, 77(12): 6401.

[24] DALIBARD J, GERBIER F, JUZELIUNAS G, et al. Colloquium: artificial gauge potentials for neutral atoms[J]. Reviews of Modern Physics, 2011, 83(4): 1523.

[25] WEI Y, ZHANG W, CUI X. Pairing superfluidity in spin-orbit coupled ultracold Fermi gases[J]. Science China (Physics, Mechanics & Astronomy), 2015(58): 1-11.

[26] LIN Y J, JIMéNEZ-GARCíA K, SPIELMAN I B. Spin-orbit-coupled Bose-Einstein condensates[J]. Nature, 2011, 471(7336): 83-88.

[27] ZHANG J Y, JI S C, CHEN Z, et al. Collective dipole oscillations of a spin-orbit coupled Bose-Einstein condensat[J]. Physical Review Letters, 2012, 109(11): 5301.

[28] WANG P, YU Z Q, FU Z, et al. Spin-orbit coupled degenerate Fermi gases[J]. Physical Review Letters, 2012, 109(9): 5301.

[29] CHEUK L W, SOMMER A T, HADZIBABIC Z, et al. Spin-injection spectroscopy of a spin-orbit coupled Fermi gas[J]. Physical Review Letters, 2012, 109(9): 5302.

[30] XU Z F, YOU L, UEDA M. Atomic spin-orbit coupling synthesized with magnetic-field-gradient pulses[J]. Physical Review A, 2013, 87(6): 3634.

[31] ANDERSON B M, SPIELMAN I B, JUZELIūNAS G. Magnetically generated spin-orbit coupling for ultracold atoms[J]. Physical Review Letters, 2013, 111(12): 5301.

[32] LUO X, WU L, CHEN J, et al. Tunable atomic spin-orbit coupling synthesized with a modulating gradient magnetic field[J]. Scientific Reports, 2016(6): 18983.

[33] HUANG L, MENG Z, WANG P, et al. Experimental realization of two-dimensional synthetic spin-orbit coupling in ultracold Fermi gases[J]. Nature Physics, 2016(12): 540.

[34] WU Z, ZHANG L, SUN W, et al. Realization of two-dimensional spin-orbit coupling for Bose-Einstein condensates[J]. Science, 2016, 354(6308): 83-88.

[35] SPIELMAN I B. Raman processes and effective gauge potenticals[J]. Physical Review A, 2009, 79(6): 3613.

[36] JUZELIUNAS G, RUSECKAS J, DALIBARD J. Generalized rashba-dresselhaus spin-orbit coupling for cold atoms[J]. Physical Review A, 2010, 81(5): 3403.

[37] CAMPBELL D L, JUZELIUNAS G, SPIELMAN I B. Realistic rashba and dresselhaus spin-orbit coupling for neutral atoms[J]. Physical Review A, 2011, 84(2): 5602.

[38] ANDERSON B M, JUZELIUNAS G, GALITSKI V M, et al. Synthetic 3D spin-orbit coupling[J]. Physical Review Letters, 2012, 108(23): 5301.

[39] BARNETT R, BOYD G R, GALITSKI V. SU(3) spin-orbit coupling in systems of ultracold atoms[J]. Physical Review Letters, 2012, 109(23): 5308.

[40] WALL M L, KOLLER A P, LI S, et al. Synthetic spin-orbit coupling in an optical lattice clock[J]. Physical Review Letters, 2016, 116(3): 5301.

[41] ZHOU X, LUO X W, CHEN G, et al. Rashba and Weyl spin-orbit coupling in an optical lattice clock[DB/OL]. (2019-01-11)[2019-02-26] https://arxiv.org/abs/1804.09282.

[42] LIVI L F, CAPPELLINI G, DIEM M, et al. Synthetic dimensions and spin-orbit coupling with an optical clock transition[J]. Physical Review Letters, 2016, 117(22): 401.

[43] KOLKOWITZ S, BROMLEY S L, BOTHWELL T, et al. Spin-orbit-coupled fermions in an optical lattice clock[J]. Nature, 2017(542): 66-70.

[44] BROMLEY S L, KOLKOWITZ S, BOTHWELL T, et al. Dynamics of interacting fermions under spin-orbit coupling in an optical lattice clock[J]. Nature Physics, 2018(14): 399.

[45] CUI X, LIAN B, HO T L, et al. Synthetic gauge eld with highly magnetic lanthanide atoms[J]. Physical Review A, 2013, 88(11): 601.

[46] BURDICK N Q, TANG Y, LEV B L. Long-lived spin-orbit-coupled degenerate dipolar Fermi gas[J]. Physical Review X, 2016(3): 1022.

[47] MANCINI M, PAGANO G, CAPPELLINI G, et al. Observation of chiral edge states with neutral fermions in synthetic Hall ribbons[J]. Science, 2015, 349(6255): 1510-1512.

[48] BLOOM B J, NICHOLSON T L, WILLIAMS J R, et al. An optical lattice clock with accuracy and stability at the 10-18level[J]. Nature, 2014, 506(7486): 71-75.

[49] BOADA O, CELI A, LATORRE J I, et al. Quantum simulation of an extra dimension[J]. Physical Review Letters, 2012, 108(13): 3001.

[50] CELI A, MASSIGNAN P, RUSECKAS J, et al. Synthetic gauge fields in synthetic dimensions[J]. Physical Review Letters, 2014, 112(4): 3001.

[51] ATALA M, AIDELSBURGER M, LOHSE M, et al. Observation of chiral currents with ultracold atoms in bosonic ladders[J]. Nature Physics, 2014(10): 588.

[52] PIRAUD M, HEIDRICH-MEISNER F, MCCULLOCH I P, et al. Vortex and Meissner phases of strongly interacting bosons on a two-leg ladder[J]. Physical Review B, 2015, 91(14): 406.

[53] NATU S S. Bosons with long-range interactions on two-leg ladders in artificial magnetic fields[J]. Physical Review A, 2015, 92(53): 623.

[54] AKATSUKA T, TAKAMOTO M, KATORI H. Three-dimensional optical lattice clock with bosonic88Sr atoms[J]. Physical Review A, 2010, 81(23): 402.

[55] CAMPBELL S L, HUTSON R B, MARTI G E, et al. A Fermi-degenerate three-dimensional optical layyice clock[J]. Science, 2017, 358(6359): 90-94.

[56] GEMELKE N, ZHANG X, HUNG C L, et al. In situ observation of incompressible mott-insulating domains in ultracold atomic gases[J]. Nature, 2009(460): 995-1002.

[57] BAKR W S, GILLEN J I, PENG A, et al. A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice[J]. Nature, 2009(462): 74-80.

[58] SHERSON J F, WEITENBERG C, ENDRES M, et al. Single-atom-resolved fluorescence imaging of an atomic Mott insulator[J]. Nature, 2010, 467(7311): 68-72.

[59] STAMPER-KURN D M, UEDA M. Spinor Bose gases: symmetries, magnetism, and quantum dynamics[J]. Reviews of Modern Physics, 2013, 85(3): 1191.

[60] SADLER L E, HIGBIE J M, LESLIE S R, et al. Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose-Einstein condensate[J]. Nature, 2006, 443(7109): 312-316.

[61] ZHOU X, PAN J S, WEI Y, et al. Interaction-induced exotic vortex states in an optical lattice clock with spin-orbit coupling[J]. Physical Review A, 2017, 96(2): 3627.

[62] ZHANG R, CHENG Y, ZHAI H, et al. Orbital feshbach resonance in alkali-earth atoms[J]. Physical Review Letters, 2015, 115(13): 5301.

[63] PAGANO G, MANCINI M, CAPPELLINI G, et al. Strongly interacting gas of two-electron fermions at an orbital feshbach resonance[J]. Physical Review Letters, 2015, 115(26): 5301.

[64] H?FER M, RIEGGER L, SCAZZA F, et al. Observation of an orbital interaction-induced feshbach resonance in173Yb[J]. Physical Review Letters, 2015, 115(26): 5302.

[65] BARBARINO S, TADDIA L, ROSSINI D, et al. Magnetic crystals and helical liquids in alkaline-earth fermionic gases[J]. Nature Communications, 2015(6): 8134.

[66] COOPER N R. Optical flux lattices for ultracold atomic gases[J]. Physical Review Letters, 2011, 106(17): 5301.

[67] GOLDMAN N, BUDICH J C, ZOLLER P. Topological quantum matter with ultracold gases in optical lattices[J]. Nature Physics, 2016(12): 639-645.

[68] CAZALILLA M A, REY A M. Ultracold fermi gases with emergent SU(N) symmetry[J]. Reports on Progress in Physics, 2014, 77(12): 4401.

[69] LI J R, LEE J, HUANG W J, et al. A stripe phase with supersolid properties in spin-orbit-coupled Bose-Einstein condensates[J]. Nature, 2017(543): 91-94.

[70] WANG C J, GAO C, JIAN C M, et al. Spin-orbit coupled spinor Bose-Einstein condensates[J]. Physical Review Letters, 2010, 105(16): 403.

[71] HO T L, ZHANG S. Bose-Einstein condensates with spin-orbit interaction[J]. Physical Review Letters, 2011, 107(15): 403.

[72] HAN W, ZHANG X F, SONG S W, et al. Double-quantum spin vortices in SU(3) spin-orbit-coupled Bose gases[J]. Physical Review A, 2016, 94(33): 629.

Brief introduction of spin-orbit coupling in optical lattice clock

WANG Lin-xue1,2,3, GUO Hui1,2,3, LIU Tao1,2,3, ZHANG Xiao-fei1,2,3

(1. National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China;2. Key Laboratory of Time and Frequency Primary Standards, Chinese Academy of Sciences, Xi’an 710600, China;3. School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 101048, China)

Based on the recent experimental realization of spin-orbit coupling in optical lattice clocks, we briefly introduce the experimental scheme for the generation of spin-orbit coupling. By comparing the optical-clock scheme and the traditional Raman scheme, we indicate the advantage of the former. We also discuss possible novel states of matter and quantum phenomena in the quantum degenerate regions, with emphasis on the important role played by the optical lattice clock in preparing, controlling and measuring new states of matter in ultra-cold atomic gases.

optical lattice clock; spin-orbit coupling; ultra-cold atomic gas; novel quantum state

10.13875/j.issn.1674-0637.2020-01-0001-08

2019-05-17；

2019-06-18

國家自然科學(xué)基金資助項(xiàng)目（11775253；11704383）

王林雪，女，博士，主要從事冷原子物理研究。