|
|
Suppressing laser phase noise in an optomechanical system |
Yexiong Zeng1, Biao Xiong2, Chong Li1( ) |
1. School of Physics, Dalian University of Technology, Dalian 116024, China 2. College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China |
|
|
Abstract We propose a scheme to suppress the laser phase noise without increasing the optomechanical singlephoton coupling strength. In the scheme, the parametric amplification terms, created by Kerr and Duffing nonlinearities, can restrain laser phase noise and strengthen the effective optomechanical coupling, respectively. Interestingly, decreasing laser phase noise leads to increasing thermal noise, which is inhibited by bringing in a broadband-squeezed vacuum environment. To reflect the superiority of the scheme, we simulate quantum memory and stationary optomechanical entanglement as examples, and the corresponding numerical results demonstrate that the laser phase noise is extremely suppressed. Our method can pave the way for studying other quantum phenomena.
|
Keywords
optomechanical system
quantum entanglement
quantum memory
|
Corresponding Author(s):
Chong Li
|
Issue Date: 23 August 2021
|
|
1 |
M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86(4), 1391 (2014)
https://doi.org/10.1103/RevModPhys.86.1391
|
2 |
T. J. Kippenberg and K. J. Vahala, Cavity optomechanics: Back-action at the mesoscale, Science321(5893), 1172 (2008)
https://doi.org/10.1126/science.1156032
|
3 |
A. Naik, O. Buu, M. D. LaHaye, A. D. Armour, A. A. Clerk, M. P. Blencowe, and K. C. Schwab, Cooling a nanomechanical resonator with quantum back-action, Nature443(7108), 193 (2006)
https://doi.org/10.1038/nature05027
|
4 |
J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, Strong and tunable nonlinear optomechanical coupling in a low-loss system, Nat. Phys. 6(9), 707 (2010)
https://doi.org/10.1038/nphys1707
|
5 |
Y. S. Park and H. Wang, Resolved-sideband and cryogenic cooling of an optomechanical resonator, Nat. Phys. 5(7), 489 (2009)
https://doi.org/10.1038/nphys1303
|
6 |
P. Rodgers, Mirror finish, Nat. Mater. 9(S1), S20 (2010)
https://doi.org/10.1038/nmat2660
|
7 |
M. R. Vanner, Selective linear or quadratic optomechanical coupling via measurement, Phys. Rev. X1(2), 021011 (2011)
https://doi.org/10.1103/PhysRevX.1.021011
|
8 |
V. Macrì, A. Ridolfo, O. Di Stefano, A. F. Kockum, F. Nori, and S. Savasta, Nonperturbative dynamical Casimir effect in optomechanical systems: Vacuum Casimir-Rabi splittings, Phys. Rev. X8(1), 011031 (2018)
https://doi.org/10.1103/PhysRevX.8.011031
|
9 |
T. K. Paraïso, M. Kalaee, L. Zang, H. Pfeifer, F. Marquardt, and O. Painter, Position-squared coupling in a tunable photonic crystal optomechanical cavity, Phys. Rev. X5(4), 041024 (2015)
https://doi.org/10.1103/PhysRevX.5.041024
|
10 |
M. Cirio, K. Debnath, N. Lambert, and F. Nori, Amplified optomechanical transduction of virtual radiation pressure, Phys. Rev. Lett.119(5), 053601 (2017)
https://doi.org/10.1103/PhysRevLett.119.053601
|
11 |
J. H. Liu, Y. B. Zhang, Y. F. Yu, and Z. M. Zhang, Photonphonon squeezing and entanglement in a cavity optomechanical system with a flying atom, Front. Phys.14(1), 12601 (2019)
https://doi.org/10.1007/s11467-018-0861-4
|
12 |
Z. R. Zhong, X. Wang, and W. Qin, Towards quantum entanglement of micromirrors via a two-level atom and radiation pressure, Front. Phys.13(5), 130319 (2018)
https://doi.org/10.1007/s11467-018-0824-9
|
13 |
K. C. Schwab and M. L. Roukes, Putting mechanics into quantum mechanics, Phys. Today58(7), 36 (2005)
https://doi.org/10.1063/1.2012461
|
14 |
C. Reinhardt, T. Müller, A. Bourassa, and J. C. Sankey, Ultralow-noise SiN trampoline resonators for sensing and optomechanics, Phys. Rev. X6(2), 021001 (2016)
https://doi.org/10.1103/PhysRevX.6.021001
|
15 |
S. Forstner, S. Prams, J. Knittel, E. D. van Ooijen, J. D. Swaim, G. I. Harris, A. Szorkovszky, W. P. Bowen, and H. Rubinsztein-Dunlop, Cavity optomechanical magnetometer, Phys. Rev. Lett.108(12), 120801 (2012)
https://doi.org/10.1103/PhysRevLett.108.120801
|
16 |
Z. Zhang, J. Pei, Y.-P. Wang, and X. Wang, Measuring orbital angular momentum of vortex beams in optomechanics, Front. Phys.16(3), 32503 (2021)
https://doi.org/10.1007/s11467-020-1030-0
|
17 |
J. Q. Liao and L. Tian, Macroscopic quantum superposition in cavity optomechanics, Phys. Rev. Lett.116(16), 163602 (2016)
https://doi.org/10.1103/PhysRevLett.116.163602
|
18 |
J. Q. Liao, Q. Q. Wu, and F. Nori, Entangling two macroscopic mechanical mirrors in a two-cavity optomechanical system, Phys. Rev. A89(1), 014302 (2014)
https://doi.org/10.1103/PhysRevA.89.014302
|
19 |
E. E. Wollman, C. U. Lei, A. J. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, and K. C. Schwab, Quantum squeezing of motion in a mechanical resonator, Science349(6251), 952 (2015)
https://doi.org/10.1126/science.aac5138
|
20 |
B. Xiong, X. Li, S. L. Chao, Z. Yang, W. Z. Zhang, W. Zhang, and L. Zhou, Strong mechanical squeezing in an optomechanical system based on Lyapunov control, Photon. Res.8(2), 151 (2020)
https://doi.org/10.1364/PRJ.8.000151
|
21 |
X. B. Yan, H. L. Lu, F. Gao, and L. Yang, Perfect optical nonreciprocity in a double-cavity optomechanical system, Front. Phys.14(5), 52601 (2019)
https://doi.org/10.1007/s11467-019-0922-3
|
22 |
A. A. Clerk, F. Marquardt, and J. G. E. Harris, Quantum measurement of phonon shot noise, Phys. Rev. Lett.104(21), 213603 (2010)
https://doi.org/10.1103/PhysRevLett.104.213603
|
23 |
P. Rabl, S. J. Kolkowitz, F. H. L. Koppens, J. G. E. Harris, P. Zoller, and M. D. Lukin, A quantum spin transducer based on nanoelectromechanical resonator arrays, Nat. Phys.6(8), 602 (2010)
https://doi.org/10.1038/nphys1679
|
24 |
X. W. Xu and Y. Li, Optical nonreciprocity and optomechanical circulator in three-mode optomechanical systems, Phys. Rev. A 91(5), 053854 (2015)
https://doi.org/10.1103/PhysRevA.91.053854
|
25 |
L. N. Song, Q. Zheng, X. W. Xu, C. Jiang, and Y. Li, Optimal unidirectional amplification induced by optical gain in optomechanical systems, Phys. Rev. A 100(4), 043835 (2019)
https://doi.org/10.1103/PhysRevA.100.043835
|
26 |
W. Li, P. Piergentili, J. Li, S. Zippilli, R. Natali, N. Malossi, G. Di Giuseppe, and D. Vitali, Noise robustness of synchronization of two nanomechanical resonators coupled to the same cavity field, Phys. Rev. A 101(1), 013802 (2020)
https://doi.org/10.1103/PhysRevA.101.013802
|
27 |
H. Jing, Ş. K. Özdemir, Z. Geng, J. Zhang, X. Y. Lü, B. Peng, L. Yang, and F. Nori, Optomechanically-induced transparency in parity-time-symmetric microresonators, Sci. Rep.5(1), 9663 (2015)
https://doi.org/10.1038/srep09663
|
28 |
H. Jing, Ş. K. Özdemir, H. Lü, and F. Nori, High-order exceptional points in optomechanics, Sci. Rep.7(1), 3386 (2017)
https://doi.org/10.1038/s41598-017-03546-7
|
29 |
Y. X. Zeng, J. Shen, M. S. Ding, and C. Li, Macroscopic Schrödinger cat state swapping in optomechanical system, Opt. Express 28(7), 9587 (2020)
https://doi.org/10.1364/OE.385814
|
30 |
Y. X. Zeng, T. Gebremariam, J. Shen, B. Xiong, and C. Li, Application of machine learning for predicting strong phonon blockade, Appl. Phys. Lett.118(16), 164003 (2021)
https://doi.org/10.1063/5.0035498
|
31 |
X. Y. Lü, W. M. Zhang, S. Ashhab, Y. Wu, and F. Nori, Quantum-criticality-induced strong Kerr nonlinearities in optomechanical systems, Sci. Rep.3(1), 2943 (2013)
https://doi.org/10.1038/srep02943
|
32 |
J. R. Johansson, G. Johansson, and F. Nori, Optomechanical-like coupling between superconducting resonators, Phys. Rev. A 90(5), 053833 (2014)
https://doi.org/10.1103/PhysRevA.90.053833
|
33 |
M. M. Zhao, Z. Qian, B. P. Hou, Y. Liu, and Y. H. Zhao, Optomechanical properties of a degenerate nonperiodic cavity chain, Front. Phys.14(2), 22601 (2019)
https://doi.org/10.1007/s11467-019-0898-z
|
34 |
M. Asjad, G. S. Agarwal, M. S. Kim, P. Tombesi, G. D. Giuseppe, and D. Vitali, Robust stationary mechanical squeezing in a kicked quadratic optomechanical system, Phys. Rev. A89(2), 023849 (2014)
https://doi.org/10.1103/PhysRevA.89.023849
|
35 |
E. J. Kim, J. R. Johansson, and F. Nori, Circuit analog of quadratic optomechanics, Phys. Rev. A91(3), 033835 (2015)
https://doi.org/10.1103/PhysRevA.91.033835
|
36 |
W. Z. Zhang, L. B. Chen, J. Cheng, and Y. F. Jiang, Quantum-correlation-enhanced weak-field detection in an optomechanical system, Phys. Rev. A 99(6), 063811 (2019)
https://doi.org/10.1103/PhysRevA.99.063811
|
37 |
B. Xiong, X. Li, S. L. Chao, Z. Yang, R. Peng, and L. Zhou, Strong squeezing of duffing oscillator in a highly dissipative optomechanical cavity system, Ann. Phys. (Berlin)532(4), 1900596 (2020)
https://doi.org/10.1002/andp.201900596
|
38 |
B. Xiong, X. Li, S. L. Chao, and L. Zhou, Optomechanical quadrature squeezing in the non-Markovian regime, Opt. Lett.43(24), 6053 (2018)
https://doi.org/10.1364/OL.43.006053
|
39 |
D. G. Lai, X. Wang, W. Qin, B. P. Hou, F. Nori, and J. Q. Liao, Tunable optomechanically induced transparency by controlling the dark-mode effect, Phys. Rev. A 102(2), 023707 (2020)
https://doi.org/10.1103/PhysRevA.102.023707
|
40 |
H. Wang, X. Gu, Y. X. Liu, A. Miranowicz, and F. Nori, Tunable photon blockade in a hybrid system consisting of an optomechanical device coupled to a two-level system, Phys. Rev. A92(3), 033806 (2015)
https://doi.org/10.1103/PhysRevA.92.033806
|
41 |
J.Q. Liao, K. Jacobs, F. Nori, and R. W. Simmonds, Modulated electromechanics: Large enhancements of nonlinearities, New J. Phys.16, 072001 (2014)
https://doi.org/10.1088/1367-2630/16/7/072001
|
42 |
J. Q. Liao, J. F. Huang, L. Tian, L. M. Kuang, and C. P. Sun, Generalized ultrastrong optomechanical-like coupling, Phys. Rev. A101(6), 063802 (2020)
https://doi.org/10.1103/PhysRevA.101.063802
|
43 |
Y. C. Liu, Y. F. Xiao, X. Luan, and C. W. Wong, Dynamic dissipative cooling of a mechanical resonator in strong coupling optomechanics, Phys. Rev. Lett.110(15), 153606 (2013)
https://doi.org/10.1103/PhysRevLett.110.153606
|
44 |
Y. C. Liu, Y. F. Xiao, X. Luan, Q. Gong, and C. W. Wong, Coupled cavities for motional ground-state cooling and strong optomechanical coupling, Phys. Rev. A 91(3), 033818 (2015)
https://doi.org/10.1103/PhysRevA.91.033818
|
45 |
M. Wang, X. Y. Lü, Y. D. Wang, J. Q. You, and Y. Wu, Macroscopic quantum entanglement in modulated optomechanics, Phys. Rev. A 94(5), 053807 (2016)
https://doi.org/10.1103/PhysRevA.94.053807
|
46 |
X. Y. Zhang, Y. Q. Guo, P. Pei, and X. X. Yi, Optomechanically induced absorption in parity–time-symmetric optomechanical systems, Phys. Rev. A95(6), 063825 (2017)
https://doi.org/10.1103/PhysRevA.95.063825
|
47 |
X. Y. Zhang, Y. H. Zhou, Y. Q. Guo, and X. X. Yi, Optomechanically induced transparency in optomechanics with both linear and quadratic coupling, Phys. Rev. A 98(5), 053802 (2018)
https://doi.org/10.1103/PhysRevA.98.053802
|
48 |
A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, Resolved-sideband cooling of a micromechanical oscillator, Nat. Phys. 4(5), 415 (2008)
https://doi.org/10.1038/nphys939
|
49 |
G. A. Phelps and P. Meystre, Laser phase noise effects on the dynamics of optomechanical resonators, Phys. Rev. A83(6), 063838 (2011)
https://doi.org/10.1103/PhysRevA.83.063838
|
50 |
A. Dalafi and M. H. Naderi, Dispersive interaction of a Bose-Einstein condensate with a movable mirror of an optomechanical cavity in the presence of laser phase noise, Phys. Rev. A 94, 063636 (2016)
https://doi.org/10.1103/PhysRevA.94.063636
|
51 |
L. Diósi, Laser linewidth hazard in optomechanical cooling, Phys. Rev. A 78(2), 021801 (2008)
https://doi.org/10.1103/PhysRevA.78.021801
|
52 |
Z. Q. Yin, Phase noise and laser-cooling limits of optomechanical oscillators, Phys. Rev. A80(3), 033821 (2009)
https://doi.org/10.1103/PhysRevA.80.033821
|
53 |
F. Farman and A. R. Bahrampour, Effects of optical parametric amplifier pump phase noise on the cooling of optomechanical resonators, J. Opt. Soc. Am. B30(7), 1898 (2013)
https://doi.org/10.1364/JOSAB.30.001898
|
54 |
P. Rabl, C. Genes, K. Hammerer, and M. Aspelmeyer, Phase-noise induced limitations on cooling and coherent evolution in optomechanical systems, Phys. Rev. A 80(6), 063819 (2009)
https://doi.org/10.1103/PhysRevA.80.063819
|
55 |
N. Meyer, A. R. Sommer, P. Mestres, J. Gieseler, V. Jain, L. Novotny, and R. Quidant, Resolved-sideband cooling of a levitated nanoparticle in the presence of laser phase noise, Phys. Rev. Lett.123(15), 153601 (2019)
https://doi.org/10.1103/PhysRevLett.123.153601
|
56 |
B. He, L. Yang, Q. Lin, and M. Xiao, Radiation pressure cooling as a quantum dynamical process, Phys. Rev. Lett.118(23), 233604 (2017)
https://doi.org/10.1103/PhysRevLett.118.233604
|
57 |
W. Wieczorek, S. G. Hofer, J. Hoelscher-Obermaier, R. Riedinger, K. Hammerer, and M. Aspelmeyer, Optimal state estimation for cavity optomechanical systems, Phys.Rev. Lett.114(22), 223601 (2015)
https://doi.org/10.1103/PhysRevLett.114.223601
|
58 |
A. Mehmood, S. Qamar, and S. Qamar, Effects of laser phase fluctuation on force sensing for a free particle in a dissipative optomechanical system, Phys. Rev. A 98(5), 053841 (2018)
https://doi.org/10.1103/PhysRevA.98.053841
|
59 |
A. Mehmood, S. Qamar, and S. Qamar, Force sensing in a dissipative optomechanical system in the presence of parametric amplifier’s pump phase noise, Phys. Scr.94(9), 095502 (2019)
https://doi.org/10.1088/1402-4896/ab1768
|
60 |
W. J. Gu, Y. Y. Wang, Z. Yi, W. X. Yang, and L. H. Sun, Force measurement in squeezed dissipative optomechanics in the presence of laser phase noise, Opt. Express 28(8), 12460 (2020)
https://doi.org/10.1364/OE.389854
|
61 |
A. Pontin, C. Biancofiore, E. Serra, A. Borrielli, F. S. Cataliotti, F. Marino, G. A. Prodi, M. Bonaldi, F. Marin, and D. Vitali, Frequency-noise cancellation in optomechanical systems for ponderomotive squeezing, Phys. Rev. A 89(3), 033810 (2014)
https://doi.org/10.1103/PhysRevA.89.033810
|
62 |
F. Farman and A. R. Bahrampour, Effect of laser phase noise on the fidelity of optomechanical quantum memory, Phys. Rev. A91(3), 033828 (2015)
https://doi.org/10.1103/PhysRevA.91.033828
|
63 |
M. Abdi, S. Barzanjeh, P. Tombesi, and D. Vitali, Effect of phase noise on the generation of stationary entanglement in cavity optomechanics, Phys. Rev. A 84(3), 032325 (2011)
https://doi.org/10.1103/PhysRevA.84.032325
|
64 |
R. Ghobadi, A. R. Bahrampour, and C. Simon, Optomechanical entanglement in the presence of laser phase noise, Phys. Rev. A 84(6), 063827 (2011)
https://doi.org/10.1103/PhysRevA.84.063827
|
65 |
R. Ahmed and S. Qamar, Effects of laser phase noise on optomechanical entanglement in the presence of a nonlinear Kerr downconverter, Phys. Scr.94(8), 085102 (2019)
https://doi.org/10.1088/1402-4896/ab0d99
|
66 |
X. B. Yan, Enhanced output entanglement with reservoir engineering, Phys. Rev. A96(5), 053831 (2017)
https://doi.org/10.1103/PhysRevA.96.053831
|
67 |
X. B. Yan, Z. J. Deng, X. D. Tian, and J. H. Wu, Entanglement optimization of filtered output fields in cavity optomechanics, Opt. Express 27(17), 24393 (2019)
https://doi.org/10.1364/OE.27.024393
|
68 |
D. Zhang and Q. Zheng, Effect of phase noise on the stationary entanglement of an optomechanical system with Kerr medium, Chin. Phys. Lett.30(2), 024213 (2013)
https://doi.org/10.1088/0256-307X/30/2/024213
|
69 |
D. Zhang, X. P. Zhang, and Q. Zheng, Enhancing stationary optomechanical entanglement with the Kerr medium, Chin. Phys. B 22(6), 064206 (2013)
https://doi.org/10.1088/1674-1056/22/6/064206
|
70 |
T. Kumar, A. B. Bhattacherjee, and Man Mohan, Dynamics of a movable micromirror in a nonlinear optical cavity, Phys. Rev. A 81(1), 013835 (2010)
https://doi.org/10.1103/PhysRevA.81.013835
|
71 |
S. Huang and A. Chen, Fano resonance and amplification in a quadratically coupled optomechanical system with a Kerr medium, Phys. Rev. A 101(2), 023841 (2020)
https://doi.org/10.1103/PhysRevA.101.023841
|
72 |
J. S. Zhang, M. C. Li, and A. X. Chen, Enhancing quadratic optomechanical coupling via a nonlinear medium and lasers, Phys. Rev. A 99(1), 013843 (2019)
https://doi.org/10.1103/PhysRevA.99.013843
|
73 |
X. Y. Lü, J. Q. Liao, L. Tian, and F. Nori, Steady-state mechanical squeezing in an optomechanical system via Duffing nonlinearity, Phys. Rev. A91(1), 013834 (2015)
https://doi.org/10.1103/PhysRevA.91.013834
|
74 |
V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Photonic chip-based optical frequency comb using soliton Cherenkov radiation, Science351(6271), 357 (2016)
https://doi.org/10.1126/science.aad4811
|
75 |
Z. R. Gong, H. Ian, Y. X. Liu, C. P. Sun, and F. Nori, Effective Hamiltonian approach to the Kerr nonlinearity in an optomechanical system, Phys. Rev. A 80(6), 065801 (2009)
https://doi.org/10.1103/PhysRevA.80.065801
|
76 |
R. W. Boyd, Nonlinear Optics, 3rd Ed., Academic Press, 2008
|
77 |
K. J. Vahala, Optical microcavities, Nature424(6950), 839 (2003)
https://doi.org/10.1038/nature01939
|
78 |
M. Asjad, S. Zippilli, and D. Vitali, Suppression of Stokes scattering and improved optomechanical cooling with squeezed light, Phys. Rev. A 94(5), 051801 (2016)
https://doi.org/10.1103/PhysRevA.94.051801
|
79 |
J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, Sideband cooling beyond the quantum backaction limit with squeezed light, Nature541(7636), 191 (2017)
https://doi.org/10.1038/nature20604
|
80 |
D. Felinto, C. W. Chou, J. Laurat, E. W. Schomburg, H. de Riedmatten, and H. J. Kimble, Conditional control of the quantum states of remote atomic memories for quantum networking, Nat. Phys.2(12), 844 (2006)
https://doi.org/10.1038/nphys450
|
81 |
V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, Storing optical information as a mechanical excitation in a silica optomechanical resonator, Phys. Rev. Lett.107(13), 133601 (2011)
https://doi.org/10.1103/PhysRevLett.107.133601
|
82 |
Y. D. Wang and A. A. Clerk, Using dark modes for highfidelity optomechanical quantum state transfer, New J.Phys.14(10), 105010 (2012)
https://doi.org/10.1088/1367-2630/14/10/105010
|
83 |
E. X. DeJesus and C. Kaufman, Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations, Phys. Rev. A 35(12), 5288 (1987)
https://doi.org/10.1103/PhysRevA.35.5288
|
84 |
S. Mahajan and A. Bhattacherjee, Controllable nonlinear effects in a hybrid optomechanical semiconductor microcavity containing a quantum dot and Kerr medium, J.Mod. Opt. 66(6), 652 (2019)
https://doi.org/10.1080/09500340.2018.1560510
|
85 |
V. Bhatt, P. Jha, and A. Bhattacherjee, Effect of second-order nonlinearity on quantum coherent oscillations in a quantum dot embedded in a doubly resonantsemiconductor micro-cavity, Optik (Stuttg.) 198, 163167 (2019)
https://doi.org/10.1016/j.ijleo.2019.163167
|
86 |
S. Mahajan, T. Kumar, A. Bhattacherjee, and ManMo-han, Ground-state cooling of a mechanical oscillator and detection of a weak force using a Bose-Einstein condensate, Phys. Rev. A 87(1), 013621 (2013)
https://doi.org/10.1103/PhysRevA.87.013621
|
87 |
G. Vidal and R. F. Werner, Computable measure of entanglement, Phys. Rev. A65(3), 032314 (2002)
https://doi.org/10.1103/PhysRevA.65.032314
|
88 |
X. Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, Squeezed optomechanics with phase-matched amplification and dissipation, Phys. Rev. Lett.114(9), 093602 (2015)
https://doi.org/10.1103/PhysRevLett.114.093602
|
89 |
T. S. Yin, X. Y. Lü, L. L. Zheng, M. Wang, S. Li, and Y. Wu, Nonlinear effects in modulated quantum optomechanics, Phys. Rev. A 95(5), 053861 (2017)
https://doi.org/10.1103/PhysRevA.95.053861
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|