Thermodynamics of ultrastrongly coupled light-matter systems

Philipp Pilar, Daniele De Bernardis, and Peter Rabl

Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1040 Vienna, Austria

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


We study the thermodynamic properties of a system of two-level dipoles that are coupled ultrastrongly to a single cavity mode. By using exact numerical and approximate analytical methods, we evaluate the free energy of this system at arbitrary interaction strengths and discuss strong-coupling modifications of derivative quantities such as the specific heat or the electric susceptibility. From this analysis we identify the lowest-order cavity-induced corrections to those quantities in the collective ultrastrong coupling regime and show that for even stronger interactions the presence of a single cavity mode can strongly modify extensive thermodynamic quantities of a large ensemble of dipoles. In this non-perturbative coupling regime we also observe a significant shift of the ferroelectric phase transition temperature and a characteristic broadening and collapse of the black-body spectrum of the cavity mode. Apart from a purely fundamental interest, these general insights will be important for identifying potential applications of ultrastrong-coupling effects, for example, in the field of quantum chemistry or for realizing quantum thermal machines.

► BibTeX data

► References

[1] C. Ciuti, G. Bastard, and I. Carusotto, Quantum vacuum properties of the intersubband cavity polariton field, Phys. Rev. B 72, 115303 (2005).

[2] P. Forn-Díaz, L. Lamata, E. Rico, J. Kono, and E. Solano, Ultrastrong coupling regimes of light-matter interaction, Rev. Mod. Phys. 91, 025005 (2019).

[3] A. F. Kockum, A. Miranowicz, S. De Liberato, S. Savasta, and F. Nori, Ultrastrong coupling between light and matter, Nat. Rev. Phys. 1, 19 (2019).

[4] Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, Ultrastrong Light-Matter Coupling Regime with Polariton Dots, Phys. Rev. Lett. 105, 196402 (2010).

[5] G. Scalari, C. Maissen, D. Turcinkova, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial, Science 335, 1323 (2012).

[6] D. Dietze, A. M. Andrews, P. Klang, G. Strasser, K. Unterrainer, and J. Darmo, Ultrastrong coupling of intersubband plasmons and terahertz metamaterials, Appl. Phys. Lett. 103, 201106 (2013).

[7] C. R. Gubbin, S. A. Maier, and S. Kéna-Cohen, Low-voltage polariton electroluminescence from an ultrastrongly coupled organic light-emitting diode, App. Phys. Lett. 104, 233302 (2014).

[8] Q. Zhang, M. Lou, X. Li, J. L. Reno, W. Pan, J. D. Watson, M. J. Manfra, and J. Kono, Collective non-perturbative coupling of 2D electrons with high-quality-factor terahertz cavity photons, Nature Phys. 12, 1005 (2016).

[9] A. Bayer, M. Pozimski, S. Schambeck, D. Schuh, R. Huber, D. Bougeard, and C. Lange, Terahertz Light-Matter Interaction beyond Unity Coupling Strength, Nano Lett. 17, 6340 (2017).

[10] B. Askenazi, A. Vasanelli, Y. Todorov, E. Sakat, J.-J. Greffet, G. Beaudoin, I. Sagnes, and C. Sirtori, Midinfrared Ultrastrong Light-Matter Coupling for THz Thermal Emission, ACS Photonics 4, 2550 (2017).

[11] T. Schwartz, J. A. Hutchison, C. Genet and T. W. Ebbesen, Reversible Switching of Ultrastrong Light-Molecule Coupling, Phys. Rev. Lett. 106, 196405 (2011).

[12] J. George, T. Chervy, A. Shalabney, E. Devaux, H. Hiura, C. Genet, and T. W. Ebbesen, Multiple Rabi Splittings under Ultrastrong Vibrational Coupling, Phys. Rev. Lett. 117, 153601 (2016).

[13] J. Flick, M. Ruggenthaler, H. Appel, and A. Rubio, Atoms and Molecules in Cavities: From Weak to Strong Coupling in QED Chemistry, Proc. Natl. Acad. Sci. 114, 3026 (2017).

[14] R. F. Ribeiro, L. A. Martinez-Martinez, M. Du, J. Campos-Gonzalez-Anguloand, and J. Yuen-Zhou, Polariton chemistry: controlling molecular dynamics with optical cavities, Chem. Sci. 9, 6325 (2018).

[15] V. N. Peters, S. Prayakarao, S. R. Koutsares, C. E. Bonner, and M. A. Noginov, Control of Physical and Chemical Processes with Nonlocal Metal–Dielectric Environments, ACS Photonics 6, 3039 (2019).

[16] J. A. Hutchison, T. Schwartz, C. Genet, E. Devaux, and T. W. Ebbesen, Modifying Chemical Landscapes by Coupling to Vacuum Fields, Angew. Chem., Int. Ed. 51, 1592 (2012).

[17] A. Thomas, J. George, A. Shalabney, M. Dryzhakov, S. J. Varma, J. Moran, T. Chervy, X. Zhong, E. Devaux, C. Genet, J. A. Hutchison, and T. W. Ebbesen, Ground-State Chemical Reactivity under Vibrational Coupling to the Vacuum Electromagnetic Field, Angew. Chem., Int. Ed. 55, 11462 (2016).

[18] S. Wang, A. Mika, J. A. Hutchison, C. Genet, A. Jouaiti, M. W. Hosseini, and T. W. Ebbesen, Phase Transition of a Perovskite Strongly Coupled to the Vacuum Field, Nanoscale 6, 7243 (2014).

[19] A. Canaguier-Durand, E. Devaux, J. George, Y. Pang, J. A. Hutchison, T. Schwartz, C. Genet, N. Wilhelms, J.-M. Lehn, and T. W. Ebbesen, Thermodynamics of Molecules Strongly Coupled to the Vacuum Field, Angew. Chem., Int. Ed. 52, 10533 (2013).

[20] M. H. Devoret, S. Girvin, and R. Schoelkopf, Circuit-QED: How strong can the coupling between a Josephson junction atom and a transmission line resonator be?, Ann. Phys. (NY) 16, 767 (2007).

[21] T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, and R. Gross, Circuit quantum electrodynamics in the ultrastrong-coupling regime, Nature Phys. 6, 772 (2010).

[22] P. Forn-Diaz, J. Lisenfeld, D. Marcos, J. J. Garcia-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime, Phys. Rev. Lett. 105, 237001 (2010).

[23] P. Forn-Díaz, J. J. García-Ripoll, B. Peropadre, J.-L. Orgiazzi, M. A. Yurtalan, R. Belyansky, C. M. Wilson, and A. Lupascu, Ultrastrong coupling of a single artificial atom to an electromagnetic continuum, Nature Phys. 13, 39 (2017).

[24] F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime, Nature Phys. 13, 44 (2017).

[25] R. H. Dicke, Coherence in Spontaneous Radiation Processes, Phys. Rev. 93, 99 (1954).

[26] T. Brandes, Coherent and collective quantum optical effects in mesoscopic systems, Physics Reports 408, 315 (2005).

[27] J. J. Hopfield, Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals, Phys. Rev. 112, 1555 (1958).

[28] K. Rzazewski, K. Wodkiewicz, and W. Zakowicz, Phase Transitions, Two-Level Atoms, and the $A^2$ Term, Phys. Rev. Lett. 35, 432 (1975).

[29] O. Viehmann, J. von Delft, and F. Marquardt, Superradiant Phase Transitions and the Standard Description of Circuit QED, Phys. Rev. Lett. 107, 113602 (2011).

[30] Y. Todorov and C. Sirtori, Intersubband polaritons in the electrical dipole gauge, Phys. Rev. B 85, 045304 (2012).

[31] M. Bamba, and T. Ogawa, Stability of polarizable materials against superradiant phase transition, Phys. Rev. A 90, 063825 (2014).

[32] T. Jaako, Z.-L. Xiang, J. J. Garcia-Ripoll, and P. Rabl, Ultrastrong coupling phenomena beyond the Dicke model, Phys. Rev. A 94, 033850 (2016).

[33] D. De Bernardis, T. Jaako, and P. Rabl, Cavity quantum electrodynamics in the non-perturbative regime, Phys. Rev. A 97, 043820 (2018).

[34] V. Rokaj, D. M. Welakuh, M. Ruggenthaler, and A. Rubio, Light-matter interaction in the long-wavelength limit: no ground-state without dipole self-energy, J. Phys. B: At. Mol. Opt. Phys. 51, 034005 (2018).

[35] G. M. Andolina, F. M. D. Pellegrino, V. Giovannetti, A. H. MacDonald, and M. Polini, Cavity quantum electrodynamics of strongly correlated electron systems: A no-go theorem for photon condensation, Phys. Rev. B 100, 121109(R) (2019).

[36] D. De Bernardis, P. Pilar, T. Jaako, S. De Liberato, and P. Rabl, Breakdown of gauge invariance in ultrastrong-coupling cavity QED, Phys. Rev. A 98, 053819 (2018).

[37] A. Stokes and A. Nazir, Gauge ambiguities imply Jaynes-Cummings physics remains valid in ultrastrong coupling QED, Nat. Commun. 10, 499 (2019).

[38] O. Di Stefano, A. Settineri, V. Macri, L. Garziano, R. Stassi, S. Savasta, and F. Nori, Resolution of gauge ambiguities in ultrastrong-coupling cavity QED, Nature Phys. 15, 803 (2019).

[39] M. Roth, F. Hassler, and D. P. DiVincenzo, Optimal gauge for the multimode Rabi model in circuit QED, Phys. Rev. Research 1, 033128 (2019).

[40] Y. A. Kudenko, A. P. Slivinsky, and G. M. Zaslavsky, Interatomic Coulomb interaction influence on the superradiance phase transition, Phys. Lett. A 50, 411 (1975).

[41] J. Keeling, Coulomb interactions, gauge invariance, and phase transitions of the Dicke model,J. Phys: Cond. Mat. 19, 295213 (2007).

[42] A. Vukics and P. Domokos, Adequacy of the Dicke model in cavity QED: A counter-no-go statement, Phys. Rev. A 86, 053807 (2012).

[43] T. Grießer, A. Vukics, and P. Domokos, Depolarization shift of the superradiant phase transition, Phys. Rev. A 94, 033815 (2016).

[44] A. Stokes and A. Nazir, Uniqueness of the phase transition in many-dipole cavity QED systems, arXiv:1905.10697 (2019).

[45] K. Hepp and E. H. Lieb, On the superradiant phase transition for molecules in a quantized radiation field: the Dicke maser model, Ann. Phys. 76, 360 (1973).

[46] Y. K. Wang, and F. T. Hioe, Phase Transition in the Dicke Model of Superradiance, Phys. Rev. A 7, 831 (1973).

[47] H. J. Carmichael, C. W. Gardiner, and D. F. Walls, Higher order corrections to the Dicke superradiant phase transition, Phys. Lett. A 46, 47 (1973).

[48] J. Galego, F. J. Garcia-Vidal, and J. Feist, Cavity-Induced Modifications of Molecular Structure in the Strong-Coupling Regime, Phys. Rev. X 5, 041022 (2015).

[49] J. A. Cwik, P. Kirton, S. De Liberato, and J. Keeling, Excitonic spectral features in strongly coupled organic polaritons, Phys. Rev. A 93, 033840 (2016).

[50] L. A. Martinez-Martinez, R. F. Ribeiro, J. Campos-Gonzalez-Angulo, and J. Yuen-Zhou, Can Ultrastrong Coupling Change Ground-State Chemical Reactions?, ACS Photonics 5, 167 (2018).

[51] Y. Todorov and C. Sirtori, Few-Electron Ultrastrong Light-Matter Coupling in a Quantum LC Circuit, Phys. Rev. X 4, 041031 (2014).

[52] H. J. Lipkin, N. Meshkov, and A. J. Glick, Validity of many-body approximation methods for a solvable model: (I). Exact solutions and perturbation theory, Nucl. Phys. 62, 188 (1965).

[53] M. Schuler, D. De Bernardis, A. M. Läuchli, and P. Rabl, The Vacua of Dipolar Cavity Quantum Electrodynamics, arXiv:2004.13738 (2020).

[54] M. Bamba, K. Inomata, and Y. Nakamura, Superradiant Phase Transition in a Superconducting Circuit in Thermal Equilibrium, Phys. Rev. Lett. 117, 173601 (2016).

[55] A. Settineri, O. Di Stefano, D. Zueco, S. Hughes, S. Savasta, and F. Nori, Gauge freedom, quantum measurements, and time-dependent interactions in cavity and circuit QED, arXiv:1912.08548 (2019).

[56] C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms (Wiley, New York, 1997).

[57] A. Das, K. Sengupta, D. Sen, and B. K. Chakrabarti, Infinite-range Ising ferromagnet in a time-dependent transverse magnetic field: Quench and ac dynamics near the quantum critical point, Phys. Rev. B 74, 144423 (2006).

[58] H. T. Quan and F. M. Cucchietti, Quantum fidelity and thermal phase transitions, Phys. Rev. E 79, 031101 (2009).

[59] J. Wilms, J. Vidal, F. Verstraete, and S. Dusuel, Finite-temperature mutual information in a simple phase transition, J. Stat. Mech. P01023 (2012).

[60] E. Irish, Generalized Rotating-Wave Approximation for Arbitrarily Large Coupling, Phys. Rev. Lett. 99, 173601 (2007).

[61] Q.-H. Chen, Y.-Y. Zhang, T. Liu, and K.-L. Wang, Numerically exact solution to the finite-size Dicke model, Phys. Rev. A 78, 051801(R) (2008).

[62] A. Le Boite, Theoretical methods for ultrastrong light-matter interactions, Adv. Quantum Technol. 3, 1900140 (2020).

[63] M. Aparicio Alcalde, M. Bucher, C. Emary, and T. Brandes, Thermal phase transitions for Dicke-type models in the ultrastrong-coupling limit, Phys. Rev. E 86, 012101 (2012).

[64] A. Ridolfo, S. Savasta, and M. J. Hartmann, Nonclassical Radiation from Thermal Cavities in the Ultrastrong Coupling Regime, Phys. Rev. Lett. 110, 163601 (2013).

[65] A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Thermal emission in the ultrastrong-coupling regime, Phys. Scr. 2013, 014053 (2013).

[66] T. Chervy, A. Thomas, E. Akiki, R. M. A. Vergauwe, A. Shalabney, J. George, E. Devaux, J. A. Hutchison, C. Genet, and T. W. Ebbesen, Vibro-Polaritonic IR Emission in the Strong Coupling Regime, ACS Photonics 5, 217 (2018).

[67] F. Armata, G. Calajo, T. Jaako, M. S. Kim, and P. Rabl, Harvesting Multiqubit Entanglement from Ultrastrong Interactions in Circuit Quantum Electrodynamics, Phys. Rev. Lett. 119, 183602 (2017).

[68] T. Holstein and H. Primakoff, Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet, Phys. Rev. 58, 1098 (1940).

[69] A. M. Bratkovsky and A. P. Levanyuk, Continuous Theory of Ferroelectric States in Ultrathin Films with Real Electrodes, Journal of Computational and Theoretical Nanoscience 6, 10.1166/​jctn.2009.1058 (2008).

[70] T. Jaako, J. J. Garcia-Ripoll, and P. Rabl, Ultrastrong-coupling circuit QED in the radio-frequency regime, Phys. Rev. A 100, 043815 (2019).

[71] L. Fusco, M. Paternostro, and G. De Chiara, Work extraction and energy storage in the Dicke model, Phys. Rev. E 94, 052122 (2016).

[72] Y. Ma, S. Su, and C. Sun, Quantum thermodynamic cycle with quantum phase transition, Phys. Rev. E 96, 022143 (2017).

[73] N. Cottet, S. Jezouin, L. Bretheau, P. Campagne-Ibarcq, Q. Ficheux, J. Anders, A. Auffeves, R. Azouit, P. Rouchon, and B. Huard, Observing a quantum Maxwell demon at work, Proc. Natl. Acad. Sci. 114, 7561 (2017).

[74] M. Naghiloo, J. J. Alonso, A. Romito, E. Lutz, and K. W. Murch, Information Gain and Loss for a Quantum Maxwell's Demon, Phys. Rev. Lett. 121, 030604 (2018).

[75] Y. Masuyama, K. Funo, Y. Murashita, A. Noguchi, S. Kono, Y. Tabuchi, R. Yamazaki, M. Ueda, and Y. Nakamura, Information-to-work conversion by Maxwell’s demon in a superconducting circuit quantum electrodynamical system, Nat. Commun. 9, 1291 (2018).

[76] M. A. Alcalde, E. Arias, Quantum Heat Engine and Quantum Phase Transition: through Anisotropic LMG and Full Dicke models, arXiv:1906.00292 (2019).

Cited by

[1] Yuto Ashida, Atac Imamoglu, Jerome Faist, Dieter Jaksch, Andrea Cavalleri, and Eugene Demler, "Quantum Electrodynamic Control of Matter: Cavity-Enhanced Ferroelectric Phase Transition", arXiv:2003.13695.

[2] Michael Schuler, Daniele De Bernardis, Andreas M. Läuchli, and Peter Rabl, "The Vacua of Dipolar Cavity Quantum Electrodynamics", arXiv:2004.13738.

[3] M. Salado-Mejía, R. Román-Ancheyta, F. Soto-Eguibar, and H. M. Moya-Cessa, "Spectroscopy and critical quantum thermometry in the ultrastrong coupling regime", arXiv:2009.01994.

[4] Yuto Ashida, Atac Imamoglu, and Eugene Demler, "Cavity Quantum Electrodynamics at Arbitrary Light-Matter Coupling Strengths", arXiv:2010.03583.

The above citations are from SAO/NASA ADS (last updated successfully 2020-10-19 15:23:43). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2020-10-19 15:14:43).