Nonreciprocal transition between two indirectly coupled energy levels
Xun-Wei Xu1,2(), Hai-Quan Shi2, Ai-Xi Chen2,3()
1. Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Key Laboratory for Matter Microstructure and Function of Hunan Province, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China 2. Department of Applied Physics, East China Jiaotong University, Nanchang 330013, China 3. Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China
We propose a theoretical scheme to realize nonreciprocal transition between two energy levels that can not coupled directly. Suppose they are coupled indirectly by two auxiliary levels with a cyclic four-level configuration, and the four transitions in the cyclic configuration are controlled by external fields. The indirectly transition become nonreciprocal when the time reversal symmetry of the system is broken by the synthetic magnetic flux, i.e., the total phase of the external driving fields through the cyclic four-level configuration. The nonreciprocal transition can be identified by the elimination of a spectral line in the spontaneous emission spectrum. Our work introduces a feasible way to observe nonreciprocal transition in a wide range of multi-level systems, including natural atoms or ions with parity symmetry.
H. Li , V. A. Sautenkov , Y. V. Rostovtsev , G. R. Welch , P. R. Hemmer , and M. O. Scully , Electromagnetically induced transparency controlled by a microwave field, Phys. Rev. A 80 (2), 023820 (2009) https://doi.org/10.1103/PhysRevA.80.023820
5
W. Z. Jia and L. F. Wei , Gains without inversion in quantum systems with broken parities, Phys. Rev. A 82 (1), 013808 (2010) https://doi.org/10.1103/PhysRevA.82.013808
6
P. Král , I. Thanopulos , M. Shapiro , and D. Cohen , Twostep Enantio-selective optical switch, Phys. Rev. Lett. 90 (3), 033001 (2003) https://doi.org/10.1103/PhysRevLett.90.033001
Y. X. Liu , J. Q. You , L. F. Wei , C. P. Sun , and F. Nori , Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit, Phys. Rev. Lett. 95 (8), 087001 (2005) https://doi.org/10.1103/PhysRevLett.95.087001
9
J. E. Mooij , T. P. Orlando , L. Levitov , L. Tian , C. H. van der Wal , and S. Lloyd , Josephson persistent-current qubit, Science 285 (5430), 1036 (1999) https://doi.org/10.1126/science.285.5430.1036
10
L. Zhou , L. P. Yang , Y. Li , and C. P. Sun , Quantum routing of single photons with a cyclic three-level system, Phys. Rev. Lett. 111 (10), 103604 (2013) https://doi.org/10.1103/PhysRevLett.111.103604
11
Y. X. Liu , H. C. Sun , Z. H. Peng , A. Miranowicz , J. S. Tsai , and F. Nori , Controllable microwave three-wave mixing via a single three-level superconducting quantum circuit, Sci. Rep. 4 (1), 7289 (2015) https://doi.org/10.1038/srep07289
12
Y. J. Zhao , J. H. Ding , Z. H. Peng , and Y. X. Liu , Realization of microwave amplification, attenuation, and frequency conversion using a single three-level superconducting quantum circuit, Phys. Rev. A 95 (4), 043806 (2017) https://doi.org/10.1103/PhysRevA.95.043806
13
Z. H. Wang , C. P. Sun , and Y. Li , Microwave degenerate parametric down-conversion with a single cyclic three-level system in a circuit-QED setup, Phys. Rev. A 91 (4), 043801 (2015) https://doi.org/10.1103/PhysRevA.91.043801
14
A. Barfuss , J. Kölbl , L. Thiel , J. Teissier , M. Kasperczyk , and P. Maletinsky , Phase-controlled coherent dynamics of a single spin under closed-contour interaction, Nat. Phys. 14 (11), 1087 (2018) https://doi.org/10.1038/s41567-018-0231-8
15
X. W. Xu , Y. J. Zhao , H. Wang , A. X. Chen , and Y. X. Liu , Nonreciprocal transition between two nondegenerate energy levels, Photon. Res. 9 (5), 879 (2021) https://doi.org/10.1364/PRJ.412904
16
J. Zhang , B. Peng , I. M. C. K. Özdemir , Y. X. Liu , H. Jing , X. Y. Lü , Y. L. Liu , L. Yang , and F. Nori , Giant non-linearity via breaking parity-time symmetry: A route to low-threshold phonon diodes, Phys. Rev. B 92 (11), 115407 (2015) https://doi.org/10.1103/PhysRevB.92.115407
X. W. Xu , C. Ye , Y. Li , and A. X. Chen , Enantiomericexcess determination based on nonreciprocal-transitioninduced spectral-line elimination, Phys. Rev. A 102 (3), 033727 (2020) https://doi.org/10.1103/PhysRevA.102.033727
19
N. A. Ansari , J. Gea-Banacloche , and M. S. Zubairy , Phase-sensitive amplification in a three-level atomic system, Phys. Rev. A 41 (9), 5179 (1990) https://doi.org/10.1103/PhysRevA.41.5179
20
C. A. Blockley and D. F. Walls , Intensity fluctuations in a frequency down-conversion process with three-level atoms, Phys. Rev. A 43 (9), 5049 (1991) https://doi.org/10.1103/PhysRevA.43.5049
21
H. Ritsch , P. Domokos , F. Brennecke , and T. Esslinger , Cold atoms in cavity-generated dynamical optical potentials, Rev. Mod. Phys. 85 (2), 553 (2013) https://doi.org/10.1103/RevModPhys.85.553
22
M. Brownnutt , M. Kumph , P. Rabl , and R. Blatt , Ion-trap measurements of electric-field noise near surfaces, Rev. Mod. Phys. 87 (4), 1419 (2015) https://doi.org/10.1103/RevModPhys.87.1419
23
M. Tomza , K. Jachymski , R. Gerritsma , A. Negretti , T. Calarco , Z. Idziaszek , and P. S. Julienne , Cold hybrid ionatom systems, Rev. Mod. Phys. 91 (3), 035001 (2019) https://doi.org/10.1103/RevModPhys.91.035001
24
P. Lodahl , S. Mahmoodian , S. Stobbe , A. Rauschenbeutel , P. Schneeweiss , J. Volz , H. Pichler , and P. Zoller , Chiral quantum optics, Nature 541 (7638), 473 (2017) https://doi.org/10.1038/nature21037
25
T. Ozawa , H. M. Price , A. Amo , N. Goldman , M. Hafezi , L. Lu , M. C. Rechtsman , D. Schuster , J. Simon , O. Zilberberg , and I. Carusotto , Topological photonics, Rev. Mod. Phys. 91 (1), 015006 (2019) https://doi.org/10.1103/RevModPhys.91.015006
26
S. Y. Zhu , R. C. F. Chan , and C. P. Lee , Spontaneous emission from a three-level atom, Phys. Rev. A 52 (1), 710 (1995) https://doi.org/10.1103/PhysRevA.52.710
27
S. Y. Zhu and M. O. Scully , Spectral line elimination and spontaneous emission cancellation via quantum interference, Phys. Rev. Lett. 76 (3), 388 (1996) https://doi.org/10.1103/PhysRevLett.76.388
28
V. Weisskopf and E. Wigner , Berechnung der natürlichen linienbreite auf grund der diracschen lichttheorie, Z. Phys. 63 (1-2), 54 (1930) https://doi.org/10.1007/BF01336768
29
M. O. Scully and M. S. Zubairy , Quantum Optics, Cambridge University Press, Cambridge, UK, 1997
30
H. F. Song , Y. B. Tang , S. L. Chen , L. J. Du , Y. Huang , H. Guan , and K. L. Gao , Combined experimental and theoretical probe of the branching fractions of the 4P3/2 state in 40Ca+, Phys. Rev. A 100 (5), 052505 (2019) https://doi.org/10.1103/PhysRevA.100.052505
31
P. A. Barton , C. J. S. Donald , D. M. Lucas , D. A. Stevens , A. M. Steane , and D. N. Stacey , Measurement of the lifetime of the 3d2D 5/2 state in 40Ca+, Phys. Rev. A 62 (3), 032503 (2000) https://doi.org/10.1103/PhysRevA.62.032503
32
A. Kreuter , C. Becher , G. P. T. Lancaster , A. B. Mundt , C. Russo , H. Häffner , C. Roos , W. Hänsel , F. SchmidtKaler , R. Blatt , and M. S. Safronova , Experimental and theoretical study of the 3d2D-level lifetimes of 40Ca+, Phys. Rev. A 71 (3), 032504 (2005) https://doi.org/10.1103/PhysRevA.71.032504
33
H. Shao , Y. Huang , H. Guan , Y. Qian , and K. Gao , Precision measurement of the 3d2D3/2-state lifetime in a single trapped 40Ca+, Phys. Rev. A 94 (4), 042507 (2016) https://doi.org/10.1103/PhysRevA.94.042507
34
Z. Meir , M. Sinhal , M. S. Safronova , and S. Willitsch , Combining experiments and relativistic theory for establishing accurate radiative quantities in atoms: The lifetime of the 2P 3/2 state in 40Ca+, Phys. Rev. A 101 (1), 012509 (2020) https://doi.org/10.1103/PhysRevA.101.012509
35
P. Staanum , I. S. Jensen , R. G. Martinussen , D. Voigt , and M. Drewsen , Lifetime measurement of the metastable 3d2D5/2 state in the 40Ca+ ion using the shelving technique on a few-ion string, Phys. Rev. A 69 (3), 032503 (2004) https://doi.org/10.1103/PhysRevA.69.032503
36
J. Jin and D. A. Church , Precision lifetimes for the Ca+ 4p2P levels: Experiment challenges theory at the 1% level, Phys. Rev. Lett. 70 (21), 3213 (1993) https://doi.org/10.1103/PhysRevLett.70.3213
37
S. Mannervik , J. Lidberg , L. O. Norlin , P. Royen , A. Schmitt , W. Shi , and X. Tordoir , Lifetime measurement of the metastable 4d2D3/2 level in Sr+ by optical pumping of a stored ion beam, Phys. Rev. Lett. 83 (4), 698 (1999) https://doi.org/10.1103/PhysRevLett.83.698
38
V. Letchumanan , M. A. Wilson , P. Gill , and A. G. Sinclair , Lifetime measurement of the metastable 4d2D5/2 state in 88Sr+ using a single trapped ion, Phys. Rev. A 72 (1), 012509 (2005) https://doi.org/10.1103/PhysRevA.72.012509
39
N. Yu , W. Nagourney , and H. Dehmelt , Radiative lifetime measurement of the Ba+ metastable D3/2 state, Phys. Rev. Lett. 78 (26), 4898 (1997) https://doi.org/10.1103/PhysRevLett.78.4898
40
E. A. Dijck , A. Mohanty , N. Valappol , M. N. N. Portela , L. Willmann , and K. Jungmann , Lifetime of the 5d2D5/2 level of 138Ba+ from quantum jumps with single and multiple Ba+ ions, Phys. Rev. A 97 (3), 032508 (2018) https://doi.org/10.1103/PhysRevA.97.032508
41
J. Gurell , E. Biémont , K. Blagoev , V. Fivet , P. Lundin , S. Mannervik , L. O. Norlin , P. Quinet , D. Rostohar , P. Royen , and P. Schef , Laser-probing measurements and calculations of lifetimes of the 5d2D3/2 and 5 d2D5/2 metastable levels in Ba II, Phys. Rev. A 75 (5), 052506 (2007) https://doi.org/10.1103/PhysRevA.75.052506
42
M. D. Havey , L. C. Balling , and J. J. Wright , Direct measurements of Ba+ excited-state lifetimes, Phys. Rev. A 15 (6), 2332 (1977) https://doi.org/10.1103/PhysRevA.15.2332
