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Clock frequency estimation under spontaneous emission |
Xi-Zhou Qin (秦锡洲)1, Jia-Hao Huang (黄嘉豪)1, Hong-Hua Zhong (钟宏华)1, Chaohong Lee (李朝红)1,2() |
1. TianQin Research Center & School of Physics and Astronomy, Sun Yat-Sen University (Zhuhai Campus), Zhuhai 519082, China 2. Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-Sen University (Guangzhou Campus), Guangzhou 510275, China |
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Abstract We investigate the quantum dynamics of a driven two-level system under spontaneous emission and its application in clock frequency estimation. By using the Lindblad equation to describe the system, we analytically obtain its exact solutions, which show three different regimes: Rabi oscillation, damped oscillation, and overdamped decay. From the analytical solutions, we explore how the spontaneous emission affects the clock frequency estimation. We find that under a moderate spontaneous emission rate, the transition frequency can still be inferred from the Rabi oscillation. Our results enable potential practical applications in frequency measurement and quantum control under decoherence.
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Keywords
clock frequency estimation
two-level system
spontaneous emission
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Corresponding Author(s):
Chaohong Lee (李朝红)
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Issue Date: 07 September 2017
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|
19 |
S.Weinberg, Lindblad decoherence in atomic clocks, Phys. Rev. A94(4), 042117(2016)
https://doi.org/10.1103/PhysRevA.94.042117
|
20 |
E.Barnesand S.Das Sarma, Analytically solvable driven time-dependent two-level quantum systems, Phys. Rev. Lett. 109(6), 060401(2012)
https://doi.org/10.1103/PhysRevLett.109.060401
|
21 |
L. D.Landau, On the theory of transfer of energy at collisions II, Phys. Z. Sowjetunion2, 46(1932)
|
22 |
C.Zener, Non-adiabatic crossing of energy levels, Proc. R. Soc. Lond. A137(833), 696(1932)
https://doi.org/10.1098/rspa.1932.0165
|
23 |
L.Allenand J. H.Eberly,Optical Resonance and Two- Level Atoms, New York: Dover Publications, 1987
|
24 |
R. W.Boyd, Nonlinear Optics, Boston: Academic Press, 1992
|
25 |
P.Meystre, Atom Optics, New York: Springer-Verlag, 2001
|
26 |
S.Harocheand J. M.Raimond, Exploring the Quantum: Atoms, Cavities, and Photons, New York: Oxford University Press, 2006
https://doi.org/10.1093/acprof:oso/9780198509141.001.0001
|
27 |
P. A.Ivanovand D.Porras, Adiabatic quantum metrology with strongly correlated quantum optical systems, Phys. Rev. A88(2), 023803(2013)
https://doi.org/10.1103/PhysRevA.88.023803
|
28 |
N.Malossi, M. G.Bason, M.Viteau, E.Arimondo, D.Ciampini, R.Mannella, and O.Morsch, Quantum driving of a two level system: Quantum speed limit and superadiabatic protocols – an experimental investigation, J. Phys. Conf. Ser. 442(1), 012062(2013)
https://doi.org/10.1088/1742-6596/442/1/012062
|
29 |
Z.Tian, J.Wang, H.Fan, andJ.Jing, Relativistic quantum metrology in open system dynamics, Sci. Rep. 5(1), 7946(2015)
https://doi.org/10.1038/srep07946
|
30 |
P. A.Ivanov, K.Singer, N. V.Vitanov, and D.Porras, Quantum sensors assisted by spontaneous symmetry breaking for detecting very small forces, Phys. Rev. Appl. 4(5), 054007(2015)
https://doi.org/10.1103/PhysRevApplied.4.054007
|
1 |
J. L.Hall, Nobel lecture: Defining and measuring optical frequencies, Rev. Mod. Phys. 78(4), 1279 (2006)
https://doi.org/10.1103/RevModPhys.78.1279
|
2 |
T. W.Hänsch, Nobel lecture: Passion for precision, Rev. Mod. Phys. 78(4), 1297(2006)
https://doi.org/10.1103/RevModPhys.78.1297
|
3 |
H.Margolis, Timekeepers of the future, Nat. Phys. 10(2), 82(2014)
|
4 |
M.Takamotoand H.Katori, Spectroscopy of the 1S0–3P0 clock transition of 87Sr in an optical lattice, Phys. Rev. Lett. 91(22), 223001(2003)
https://doi.org/10.1103/PhysRevLett.91.223001
|
5 |
T.Steinmetz, T.Wilken, C.Araujo-Hauck, R.Holzwarth, T. W.Hänsch, L.Pasquini, A.Manescau, S.D’Odorico, M. T.Murphy, T.Kentischer, W.Schmidt, and T.Udem, Laser frequency combs for astronomical observations, Science321(5894), 1335(2008)
https://doi.org/10.1126/science.1161030
|
6 |
M. S.Grewal,A. P.Andrews, and C. G.Bartone, Global Navigation Satellite Systems, Inertial Navigation, and Integration, New York: John Wiley & Sons, 2013
|
7 |
J.Kitching, S.Knappe, and E. A.Donley, Atomic sensors – A review, IEEE Sens. J. 11(9), 1749(2011)
https://doi.org/10.1109/JSEN.2011.2157679
|
8 |
D.Budkerand M.Romalis, Optical magnetometry, Nat. Phys. 3(4), 227(2007)
|
9 |
I. I.Rabi, Space quantization in a gyrating magnetic field, Phys. Rev. 51(8), 652(1937)
https://doi.org/10.1103/PhysRev.51.652
|
10 |
N.Hinkley, J. A.Sherman, N. B.Phillips, M.Schioppo, N. D.Lemke, K.Beloy, M.Pizzocaro,C. W.Oates, and A. D.Ludlow, An atomic clock with 10−18 instability, Science341(6151), 1215(2013)
https://doi.org/10.1126/science.1240420
|
11 |
B. J.Bloom, T. L.Nicholson, J. R.Williams, S. L.Campbell, M.Bishof, X.Zhang, W.Zhang, S. L.Bromley, and J.Ye, An optical lattice clock with accuracy and stability at the 10−18 level, Nature506(7486), 71(2014)
https://doi.org/10.1038/nature12941
|
12 |
T. L.Nicholson,S. L.Campbell, R. B.Hutson, G. E.Marti, B. J.Bloom, R. L.McNally, W.Zhang, M. D.Barrett, M. S.Safronova, G. F.Strouse, W. L.Tew, and J.Ye, Systematic evaluation of an atomic clock at 2×10−18 total uncertainty, Nat. Commun. 6, 6896(2015)
https://doi.org/10.1038/ncomms7896
|
13 |
S. G.Porsevand A.Derevianko, Multipolar theory of blackbody radiation shift of atomic energy levels and its implications for optical lattice clocks, Phys. Rev. A74(2), 020502(R) (2006)
|
14 |
A. V.Taichenachev, V. I.Yudin, V. D.Ovsiannikov, and V. G.Pal’chikov, Optical lattice polarization effects on hyperpolarizability of atomic clock transitions, Phys. Rev. Lett. 97(17), 173601(2006)
https://doi.org/10.1103/PhysRevLett.97.173601
|
15 |
K.Gibble, Decoherence and collisional frequency shifts of trapped bosons and fermions, Phys. Rev. Lett. 103(11), 113202(2009)
https://doi.org/10.1103/PhysRevLett.103.113202
|
16 |
T.Rosenband,D. B.Hume, P. O.Schmidt, C. W.Chou, A.Brusch, L.Lorini, W. H.Oskay, R. E.Drullinger, T. M.Fortier, J. E.Stalnaker,S. A.Diddams, W. C.Swann,N. R.Newbury, W. M.Itano, D. J.Wineland, and J. C.Bergquist, Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place, Science319(5871), 1808(2008)
https://doi.org/10.1126/science.1154622
|
17 |
C. W.Chou, D. B.Hume,J. C. J.Koelemeij,D. J.Wineland, and T.Rosenband, Frequency comparison of two high-accuracy Al+ optical clocks, Phys. Rev. Lett. 104(7), 070802(2010)
https://doi.org/10.1103/PhysRevLett.104.070802
|
18 |
N.Huntemann, C.Sanner, B.Lipphardt, C.Tamm, and E.Peik, Single-ion atomic clock with 3×10−18 systematic uncertainty, Phys. Rev. Lett. 116(6), 063001(2016)
https://doi.org/10.1103/PhysRevLett.116.063001
|
31 |
A.Greilich, S. E.Economou, S.Spatzek, D. R.Yakovlev, D.Reuter, A. D.Wieck, T. L.Reinecke, and M.Bayer, Ultrafast optical rotations of electron spins in quantum dots, Nat. Phys. 5(4), 262(2009)
|
32 |
E.Poem, O.Kenneth, Y.Kodriano, Y.Benny, S.Khatsevich, J. E.Avron, and D.Gershoni, Optically induced rotation of an exciton spin in a semiconductor quantum dot, Phys. Rev. Lett. 107(8), 087401(2011)
https://doi.org/10.1103/PhysRevLett.107.087401
|
33 |
M. G.Bason, M.Viteau, N.Malossi, P.Huillery, E.Arimondo, D.Ciampini, R.Fazio, V.Giovannetti, R.Mannella, and O.Morsch, High-fidelity quantum driving, Nat. Phys. 8(2), 147(2011)
|
34 |
S.Sauer, C.Gneiting, and A.Buchleitner, Optimal coherent control to counteract dissipation, Phys. Rev. Lett. 111(3), 030405(2013)
https://doi.org/10.1103/PhysRevLett.111.030405
|
35 |
D.Daems, A.Ruschhaupt, D.Sugny, and S.Guérin, Robust quantum control by a single-shot shaped pulse, Phys. Rev. Lett. 111(5), 050404(2013)
https://doi.org/10.1103/PhysRevLett.111.050404
|
36 |
Y.Wuand X.Yang, Strong-coupling theory of periodically driven two-level systems, Phys. Rev. Lett. 98(1), 013601(2007)
https://doi.org/10.1103/PhysRevLett.98.013601
|
37 |
X.Yangand Y.Wu, Weak-coupling theory for semiclassical periodically driven two-level systems: Beyoud rotating-wave approximation, Commum. Theor. Phys. 48(2), 339(2007)
https://doi.org/10.1088/0253-6102/48/2/027
|
38 |
Q.Xieand W.Hai, Analytical results for a monochromatically driven two-level system, Phys. Rev. A82(3), 032117(2010)
https://doi.org/10.1103/PhysRevA.82.032117
|
39 |
W.Hai, K.Hai, and Q.Chen, Transparent control of an exactly solvable two-level system via combined modulations, Phys. Rev. A87(2), 023403(2013)
https://doi.org/10.1103/PhysRevA.87.023403
|
40 |
E.Barnes, Analytically solvable two-level quantum systems and Landau-Zener interferometry, Phys. Rev. A88(1), 013818(2013)
https://doi.org/10.1103/PhysRevA.88.013818
|
41 |
A.Messinaand H.Nakazato, Analytically solvable Hamiltonians for quantum two-level systems and their dynamics, J. Phys. A Math. Theor. 47(44), 445302(2014)
https://doi.org/10.1088/1751-8113/47/44/445302
|
42 |
H. P.Breuerand F.Petruccione, The Theory of Open Quantum Systems, New York: Oxford University Press, 2002
|
43 |
M. A.Nielsenand I. L.Chuang, Quantum Computation and Quantum Information, Cambridge: Cambridge University Press, 2000
|
44 |
M.Grifoniand P.Hänggi, Driven quantum tunneling, Phys. Rep. 304(5–6), 229(1998)
https://doi.org/10.1016/S0370-1573(98)00022-2
|
45 |
M.Thorwart, L.Hartmann, I.Goychuk, and P.Hänggi, Controlling decoherence of a two-level atom in a lossy cavity, J. Mod. Opt. 47(14–15), 2905(2000)
https://doi.org/10.1080/09500340008232205
|
46 |
D.Mogilevtsev, A. P.Nisovtsev, S.Kilin, S. B.Cavalcanti, H. S.Brandi, and L. E.Oliveira, Drivingdependent damping of Rabi oscillations in two-level semiconductor systems, Phys. Rev. Lett. 100(1), 017401(2008)
https://doi.org/10.1103/PhysRevLett.100.017401
|
47 |
A.Sergiand K. G.Zloshchastiev, Non-Hermitian quantum dynamics of a two-level system and models of dissipative environments, Int. J. Mod. Phys. B27(27), 1350163(2013)
https://doi.org/10.1142/S0217979213501634
|
48 |
K. N.Zlatanov, G. S.Vasilev, P. A.Ivanov, and N. V.Vitanov, Exact solution of the Bloch equations for the nonresonant exponential model in the presence of dephasing, Phys. Rev. A92(4), 043404(2015)
https://doi.org/10.1103/PhysRevA.92.043404
|
49 |
M. S. P.Eastham, The Spectral Theory of Periodic Differential Equations, Edinburgh and London: Scottish Academic Press, 1973
|
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