Shortcuts to Squeezed Thermal States

Léonce Dupays1,2 and Aurélia Chenu1,2,3

1Donostia International Physics Center, E-20018 San Sebastián, Spain
2Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, G.D. Luxembourg
3Ikerbasque, Basque Foundation for Science, E-48013 Bilbao, Spain

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Abstract

Squeezed state in harmonic systems can be generated through a variety of techniques, including varying the oscillator frequency or using nonlinear two-photon Raman interaction. We focus on these two techniques to drive an initial thermal state into a final squeezed thermal state with controlled squeezing parameters – amplitude and phase – in arbitrary time. The protocols are designed through reverse engineering for both unitary and open dynamics. Control of the dissipation is achieved using stochastic processes, readily implementable via, e.g., continuous quantum measurements. Importantly, this allows controlling the state entropy and can be used for fast thermalization. The developed protocols are thus suited to generate squeezed thermal states at controlled temperature in arbitrary time.

The Heisenberg uncertainty principle prevents measuring position and momentum simultaneously with arbitrary accuracy. However, one can gain precision on position at the expense of uncertainty in momentum, or vice versa. This is known as squeezing and allows reducing the uncertainty on a chosen conjugate variable.
Squeezing is having a plethora of applications: it enhances the precision of measurement and thus helped the detection of gravitational waves and the development of atomic clocks. Knowing how to generate squeezed states in a fast way is relevant to quantum technologies, for instance in order to increase the rate of computation in information processing. In the context of quantum thermodynamics, squeezed thermal states can be used as a resource to enhance the performance of quantum engines.
Here, we design control protocols to dynamically generate squeezed thermal states in controled time at arbitrary temperature. The control of temperature is made possible thanks to engineered dissipation, that we propose, can be implemented using stochastic fields. We present control protocols for experimental implementation in a stochastically shaken harmonic trap or via two-photon Raman interaction.

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[1] J. Abadie, others, and The LIGO Scientific Collaboration, Nature Physics 7, 962 (2011).
https:/​/​doi.org/​10.1038/​nphys2083

[2] F. Wolfgramm, A. Cerè, F. A. Beduini, A. Predojević, M. Koschorreck, and M. W. Mitchell, Phys. Rev. Lett. 105, 053601 (2010).
https:/​/​doi.org/​10.1103/​PhysRevLett.105.053601

[3] E. S. Polzik, Nature 453, 45 (2008).
https:/​/​doi.org/​10.1038/​453045a

[4] H. J. Kimble and D. F. Walls, J. Opt. Soc. Am. B 4, 1449 (1987).
http:/​/​josab.osa.org/​abstract.cfm?URI=josab-4-10-1449

[5] E. S. Polzik, J. Carri, and H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
https:/​/​doi.org/​10.1103/​PhysRevLett.68.3020

[6] H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 100, 033602 (2008).
https:/​/​doi.org/​10.1103/​PhysRevLett.100.033602

[7] Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, Optics Express 15, 4321 (2007).
https:/​/​doi.org/​10.1364/​OE.15.004321

[8] C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, Optics Letters 32, 178 (2007).
https:/​/​doi.org/​10.1364/​OL.32.000178

[9] C. M. Caves, K. S. Thorne, R. W. P. Drever, V. D. Sandberg, and M. Zimmermann, Rev. Mod. Phys. 52, 341 (1980).
https:/​/​doi.org/​10.1103/​RevModPhys.52.341

[10] K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, Nature Physics 4, 472 (2008).
https:/​/​doi.org/​10.1038/​nphys920

[11] M. Tse, others, and The LIGO Scientific Collaboration, Phys. Rev. Lett. 123, 231107 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.123.231107

[12] J. Klaers, Phys. Rev. Lett. 122, 040602 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.122.040602

[13] X. L. Huang, T. Wang, and X. X. Yi, Phys. Rev. E 86, 051105 (2012).
https:/​/​doi.org/​10.1103/​PhysRevE.86.051105

[14] J. Roßnagel, O. Abah, F. Schmidt-Kaler, K. Singer, and E. Lutz, Phys. Rev. Lett. 112, 030602 (2014).
https:/​/​doi.org/​10.1103/​PhysRevLett.112.030602

[15] L. A. Correa, J. P. Palao, D. Alonso, and G. Adesso, Scientific Reports 4, 1 (2014).
https:/​/​doi.org/​10.1038/​srep03949

[16] G. Manzano, F. Galve, R. Zambrini, and J. M. R. Parrondo, Phys. Rev. E 93, 052120 (2016).
https:/​/​doi.org/​10.1103/​PhysRevE.93.052120

[17] W. Niedenzu, D. Gelbwaser-Klimovsky, A. G. Kofman, and G. Kurizki, New J. Phys. 18, 083012 (2016).
https:/​/​doi.org/​10.1088/​1367-2630/​18/​8/​083012

[18] W. Niedenzu, V. Mukherjee, A. Ghosh, A. G. Kofman, and G. Kurizki, Nature Communications 9, 1 (2018).
https:/​/​doi.org/​10.1038/​s41467-017-01991-6

[19] J. Klaers, S. Faelt, A. Imamoglu, and E. Togan, Phys. Rev. X 7, 031044 (2017).
https:/​/​doi.org/​10.1103/​PhysRevX.7.031044

[20] M. Rashid, T. Tufarelli, J. Bateman, J. Vovrosh, D. Hempston, M. S. Kim, and H. Ulbricht, Phys. Rev. Lett. 117, 273601 (2016).
https:/​/​doi.org/​10.1103/​PhysRevLett.117.273601

[21] T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
https:/​/​doi.org/​10.1126/​science.1156032

[22] P. Meystre, Annalen der Physik 525, 215 (2012).
https:/​/​doi.org/​10.1002/​andp.201200226

[23] M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
https:/​/​doi.org/​10.1103/​RevModPhys.86.1391

[24] M. Asjad, G. S. Agarwal, M. S. Kim, P. Tombesi, G. D. Giuseppe, and D. Vitali, Phys. Rev. A 89, 023849 (2014).
https:/​/​doi.org/​10.1103/​PhysRevA.89.023849

[25] G. Milburn and D. F. Walls, Optics Communications 39, 401 (1981).
https:/​/​doi.org/​10.1016/​0030-4018(81)90232-7

[26] A. Szorkovszky, A. C. Doherty, G. I. Harris, and W. P. Bowen, Phys. Rev. Lett. 107, 213603 (2011).
https:/​/​doi.org/​10.1103/​PhysRevLett.107.213603

[27] A. Szorkovszky, G. A. Brawley, A. C. Doherty, and W. P. Bowen, Phys. Rev. Lett. 110, 184301 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.110.184301

[28] C. M. Caves, Phys. Rev. D 23, 1693 (1981).
https:/​/​doi.org/​10.1103/​PhysRevD.23.1693

[29] V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne, Science 209, 547 (1980).
https:/​/​doi.org/​10.1126/​science.209.4456.547

[30] R. Ruskov, K. Schwab, and A. N. Korotkov, Phys. Rev. B 71, 235407 (2005).
https:/​/​doi.org/​10.1103/​PhysRevB.71.235407

[31] A. A. Clerk, F. Marquardt, and K. Jacobs, New J. Phys. 10, 095010 (2008).
https:/​/​doi.org/​10.1088/​1367-2630/​10/​9/​095010

[32] M. G. Genoni, S. Mancini, and A. Serafini, Phys. Rev. A 87, 042333 (2013).
https:/​/​doi.org/​10.1103/​PhysRevA.87.042333

[33] M. G. Genoni, J. Zhang, J. Millen, P. F. Barker, and A. Serafini, New J. Phys. 17, 073019 (2015a).
https:/​/​doi.org/​10.1088/​1367-2630/​17/​7/​073019

[34] M. Brunelli, D. Malz, and A. Nunnenkamp, Phys. Rev. Lett. 123, 093602 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.123.093602

[35] C. Meng, G. A. Brawley, J. S. Bennett, M. R. Vanner, and W. P. Bowen, Phys. Rev. Lett. 125, 043604 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.125.043604

[36] J. S. Bennett, L. S. Madsen, H. Rubinsztein-Dunlop, and W. P. Bowen, New J. Phys. 22, 103028 (2020).
https:/​/​doi.org/​10.1088/​1367-2630/​abb73f

[37] M.-Z. Huang, J. A. de la Paz, T. Mazzoni, K. Ott, A. Sinatra, C. L. G. Alzar, and J. Reichel, arXiv:2007.01964 (2020).
arXiv:2007.01964

[38] A. Kronwald, F. Marquardt, and A. A. Clerk, Phys. Rev. A 88, 063833 (2013).
https:/​/​doi.org/​10.1103/​PhysRevA.88.063833

[39] O. Abah and E. Lutz, EPL (Europhysics Letters) 106, 20001 (2014).
https:/​/​doi.org/​10.1209/​0295-5075/​106/​20001

[40] E. E. Wollman, C. U. Lei, A. J. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, and K. C. Schwab, Science 349, 952 (2015).
https:/​/​doi.org/​10.1126/​science.aac5138

[41] J.-M. Pirkkalainen, E. Damskägg, M. Brandt, F. Massel, and M. A. Sillanpää, Phys. Rev. Lett. 115, 243601 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.115.243601

[42] M. S. Kim, F. A. M. de Oliveira, and P. L. Knight, Phys. Rev. A 40, 2494 (1989a).
https:/​/​doi.org/​10.1103/​PhysRevA.40.2494

[43] P. Král, Phys. Rev. A 42, 4177 (1990).
https:/​/​doi.org/​10.1103/​PhysRevA.42.4177

[44] D. F. Walls, Nature 306, 141 (1983).
https:/​/​doi.org/​10.1038/​306141a0

[45] A. del Campo and K. Kim, New J. Phys. 21, 050201 (2019).
https:/​/​doi.org/​10.1088/​1367-2630/​ab1437

[46] X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 104, 063002 (2010).
https:/​/​doi.org/​10.1103/​PhysRevLett.104.063002

[47] G. Vacanti, R. Fazio, S. Montangero, G. M. Palma, M. Paternostro, and V. Vedral, New J. Phys. 16, 053017 (2014).
https:/​/​doi.org/​10.1088/​1367-2630/​16/​5/​053017

[48] S. Alipour, A. Chenu, A. T. Rezakhani, and A. del Campo, Quantum 4, 336 (2020).
https:/​/​doi.org/​10.22331/​q-2020-09-28-336

[49] R. Dann, A. Tobalina, and R. Kosloff, Phys. Rev. Lett. 122, 250402 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.122.250402

[50] T. Villazon, A. Polkovnikov, and A. Chandran, Phys. Rev. A 100, 012126 (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.100.012126

[51] L. Dupays, I. L. Egusquiza, A. del Campo, and A. Chenu, Phys. Rev. Research 2, 033178 (2020).
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.033178

[52] R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University Press, Oxford, 2000).

[53] L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

[54] G. D. Mahan, Many-Particle Physics, 3rd ed. (Kluwer Academic Publishers, 2000).

[55] A. Chenu, S.-Y. Shiau, and M. Combescot, Phys. Rev. B 99, 014302 (2019).
https:/​/​doi.org/​10.1103/​PhysRevB.99.014302

[56] J. G. Muga, X. Chen, S. Ibáñez, I. Lizuain, and A. Ruschhaupt, J. Physics B: Atomic, Molecular and Optical Physics 43, 085509 (2010).
https:/​/​doi.org/​10.1088/​0953-4075/​43/​8/​085509

[57] A. del Campo, Phys. Rev. Lett. 111, 100502 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.111.100502

[58] K. Funo, J.-N. Zhang, C. Chatou, K. Kim, M. Ueda, and A. del Campo, Phys. Rev. Lett. 118, 100602 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.118.100602

[59] C. F. Lo, J. Physics A: Mathematical and General 23, 1155 (1990).
https:/​/​doi.org/​10.1088/​0305-4470/​23/​7/​021

[60] D. J. Heinzen and D. J. Wineland, Phys. Rev. A 42, 2977 (1990).
https:/​/​doi.org/​10.1103/​PhysRevA.42.2977

[61] H.-K. Lau and D. F. V. James, Phys. Rev. A 85, 062329 (2012).
https:/​/​doi.org/​10.1103/​PhysRevA.85.062329

[62] D. Wineland, C. Monroe, W. Itano, D. Leibfried, B. King, and D. Meekhof, J. Res. Natl. Inst. Stand. Tech. 103, 259 (1998).
https:/​/​doi.org/​10.6028/​jres.103.019

[63] M. A. Lohe, J. Physics A: Mathematical and Theoretical 42, 035307 (2009).
https:/​/​doi.org/​10.1088/​1751-8113/​42/​3/​035307

[64] V. P. Ermakov, Univ. Izv. Kiev Ser. III 9, 1 (1880), Appl. Anal. Discrete Math. 2, 123 (2008 Engl. Transl.).

[65] S. Deffner, C. Jarzynski, and A. del Campo, Phys. Rev. X 4, 021013 (2014).
https:/​/​doi.org/​10.1103/​PhysRevX.4.021013

[66] W. Ketterle and D. E. Pritchard, Phys. Rev. A 46, 4051 (1992).
https:/​/​doi.org/​10.1103/​PhysRevA.46.4051

[67] M. Kim, M. G. Kim, and K. Lee, J. Modern Optics 41, 569 (1994),.
https:/​/​doi.org/​10.1080/​09500349414550551

[68] E. Joos and H. D. Zeh, Zeitschrift für Physik B Condensed Matter 59, 223 (1985).
https:/​/​doi.org/​10.1007/​BF01725541

[69] M. Schlosshauer, Decoherence and the Quantum-to-Classical Transition (Springer, Berlin, 2007).
https:/​/​doi.org/​10.1007/​978-3-540-35775-9

[70] P. Meystre and M. Zubairy, Physics Letters A 89, 390 (1982).
https:/​/​doi.org/​10.1016/​0375-9601(82)90330-9

[71] J. R. Kukliński and J. L. Madajczyk, Phys. Rev. A 37, 3175 (1988).
https:/​/​doi.org/​10.1103/​PhysRevA.37.3175

[72] C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge University Press, 2004).
https:/​/​doi.org/​10.1017/​CBO9780511791239

[73] R. Glauber, Proc. Int. School of Physics’ Enrico Fermi’Course 118 (1992).

[74] D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Rev. Mod. Phys. 75, 281 (2003).
https:/​/​doi.org/​10.1103/​RevModPhys.75.281

[75] E. Brion, L. H. Pedersen, and K. Mølmer, J. Physics A: Mathematical and Theoretical 40, 1033 (2007).
https:/​/​doi.org/​10.1088/​1751-8113/​40/​5/​011

[76] I. Lizuain, J. G. Muga, and J. Eschner, Phys. Rev. A 77, 053817 (2008).
https:/​/​doi.org/​10.1103/​PhysRevA.77.053817

[77] K. Jacobs and D. A. Steck, Contemporary Physics 47, 279 (2006).
https:/​/​doi.org/​10.1080/​00107510601101934

[78] N. H. McCoy, Proceedings of the Edinburgh Mathematical Society 3, 118 (1932).
https:/​/​doi.org/​10.1017/​S0013091500013870

[79] P. C. Haljan, K.-A. Brickman, L. Deslauriers, P. J. Lee, and C. Monroe, Phys. Rev. Lett. 94, 153602 (2005).
https:/​/​doi.org/​10.1103/​PhysRevLett.94.153602

[80] I. Saideh, D. Finkelstein-Shapiro, T. o. Pullerits, and A. Keller, Phys. Rev. A 102, 032212 (2020).
https:/​/​doi.org/​10.1103/​PhysRevA.102.032212

[81] D. Finkelstein-Shapiro, D. Viennot, I. Saideh, T. Hansen, T. Pullerits, and A. Keller, Phys. Rev. A 101, 042102 (2020).
https:/​/​doi.org/​10.1103/​PhysRevA.101.042102

[82] F. Reiter and A. S. Sørensen, Phys. Rev. A 85, 032111 (2012).
https:/​/​doi.org/​10.1103/​PhysRevA.85.032111

[83] M. G. Genoni, M. Bina, S. Olivares, G. D. Chiara, and M. Paternostro, New J. Phys. 17, 013034 (2015b).
https:/​/​doi.org/​10.1088/​1367-2630/​17/​1/​013034

[84] H. Seifoory, S. Doutre, M. M. Dignam, and J. E. Sipe, J. Opt. Soc. Am. B 34, 1587 (2017).
https:/​/​doi.org/​10.1364/​JOSAB.34.001587

[85] R. T. Sutherland, S. C. Burd, D. H. Slichter, S. B. Libby, and D. Leibfried, arXiv:2103.05832 (2021).
arXiv:2103.05832

[86] Y. Rezek and R. Kosloff, New J. Phys. 8, 83 (2006).
https:/​/​doi.org/​10.1088/​1367-2630/​8/​5/​083

[87] M. Born, W. Heisenberg, and P. Jordan, Zeitschrift für Physik 35, 557 (1926).
https:/​/​doi.org/​10.1007/​BF01379806

[88] S. L. Adler, Phys. Rev. D 67, 025007 (2003).
https:/​/​doi.org/​10.1103/​PhysRevD.67.025007

[89] S. V. Lawande and A. Joshi, Phys. Rev. A 50, 1692 (1994).
https:/​/​doi.org/​10.1103/​PhysRevA.50.1692

[90] Q. Qiu, S. Tao, C. Liu, S. Guan, M. Xie, and B. Fan, Phys. Rev. A 96, 063808 (2017).
https:/​/​doi.org/​10.1103/​PhysRevA.96.063808

[91] M. Scala, B. Militello, A. Messina, J. Piilo, and S. Maniscalco, Phys. Rev. A 75, 013811 (2007a).
https:/​/​doi.org/​10.1103/​PhysRevA.75.013811

[92] M. Scala, B. Militello, A. Messina, S. Maniscalco, J. Piilo, and K.-A. Suominen, J. Physics A: Mathematical and Theoretical 40, 14527 (2007b).
https:/​/​doi.org/​10.1088/​1751-8113/​40/​48/​015

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[3] Léonce Dupays, David C. Spierings, Aephraim M. Steinberg, and Adolfo del Campo, "Delta-kick cooling, time-optimal control of scale-invariant dynamics, and shortcuts to adiabaticity assisted by kicks", Physical Review Research 3 3, 033261 (2021).

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