Quantum Phase Transitions in Optomechanical Systems
Abstract: In this letter, we investigate the ground state properties of an optomechanical system consisting of a coupled cavity and mechanical modes. An exact solution is given when the ratio $\eta$ between the cavity and mechanical frequencies tends to infinity. This solution reveals a coherent photon occupation in the ground state by breaking continuous or discrete symmetries, exhibiting an equilibrium quantum phase transition (QPT). In the $U(1)$-broken phase, an unstable Goldstone mode can be excited. In the model featuring $Z_2$ symmetry, we discover the mutually (in the finite $\eta$) or unidirectionally (in $\eta \rightarrow \infty$) dependent relation between the squeezed vacuum of the cavity and mechanical modes. In particular, when the cavity is driven by a squeezed field along the required squeezing parameter, it enables modifying the region of $Z_2$-broken phase and significantly reducing the coupling strength to reach QPTs. Furthermore, by coupling atoms to the cavity mode, the hybrid system can undergo a QPT at a hybrid critical point, which is cooperatively determined by the optomechanical and light-atom systems. These results suggest that this optomechanical system complements other phase transition models for exploring novel critical phenomena.
- S. Sachdev, Quantum Phase Transitions, 2nd ed. (Cambridge University Press, Cambridge, England, 2011).
- M. Vojta, Quantum phase transitions, Reports on Progress in Physics 66, 2069 (2003).
- P. W. Higgs, Broken symmetries and the masses of gauge bosons, Phys. Rev. Lett. 13, 508 (1964).
- K. Hepp and E. H. Lieb, On the superradiant phase transition for molecules in a quantized radiation field: the Dicke maser model, Annals of Physics 76, 360 (1973).
- Y. K. Wang and F. T. Hioe, Phase transition in the Dicke model of superradiance, Phys. Rev. A 7, 831 (1973).
- C. Emary and T. Brandes, Chaos and the quantum phase transition in the Dicke model, Phys. Rev. E 67, 066203 (2003).
- S. Ashhab, Superradiance transition in a system with a single qubit and a single oscillator, Phys. Rev. A 87, 013826 (2013).
- M.-J. Hwang, R. Puebla, and M. B. Plenio, Quantum phase transition and universal dynamics in the Rabi model, Phys. Rev. Lett. 115, 180404 (2015).
- M.-J. Hwang and M. B. Plenio, Quantum phase transition in the finite Jaynes-Cummings lattice systems, Phys. Rev. Lett. 117, 123602 (2016).
- A. Baksic and C. Ciuti, Controlling discrete and continuous symmetries in “superradiant” phase transitions with circuit QED systems, Phys. Rev. Lett. 112, 173601 (2014).
- I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86, 153 (2014).
- J. Vidal and S. Dusuel, Finite-size scaling exponents in the Dicke model, Europhysics Letters 74, 817 (2006).
- L. Bakemeier, A. Alvermann, and H. Fehske, Quantum phase transition in the Dicke model with critical and noncritical entanglement, Phys. Rev. A 85, 043821 (2012).
- N. Lambert, C. Emary, and T. Brandes, Entanglement and the phase transition in single-mode superradiance, Phys. Rev. Lett. 92, 073602 (2004).
- D. Guerci, P. Simon, and C. Mora, Superradiant phase transition in electronic systems and emergent topological phases, Phys. Rev. Lett. 125, 257604 (2020).
- G. Mazza and A. Georges, Superradiant quantum materials, Phys. Rev. Lett. 122, 017401 (2019).
- G. Chiriacò, M. Dalmonte, and T. Chanda, Critical light-matter entanglement at cavity mediated phase transitions, Phys. Rev. B 106, 155113 (2022).
- J. Zhao and M.-J. Hwang, Frustrated superradiant phase transition, Phys. Rev. Lett. 128, 163601 (2022).
- M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
- G. Via, G. Kirchmair, and O. Romero-Isart, Strong single-photon coupling in superconducting quantum magnetomechanics, Phys. Rev. Lett. 114, 143602 (2015).
- O. Shevchuk, G. A. Steele, and Y. M. Blanter, Strong and tunable couplings in flux-mediated optomechanics, Phys. Rev. B 96, 014508 (2017).
- L. Neumeier, T. E. Northup, and D. E. Chang, Reaching the optomechanical strong-coupling regime with a single atom in a cavity, Phys. Rev. A 97, 063857 (2018).
- M. Kounalakis, Y. M. Blanter, and G. A. Steele, Flux-mediated optomechanics with a transmon qubit in the single-photon ultrastrong-coupling regime, Phys. Rev. Res. 2, 023335 (2020).
- I. Rodrigues, D. Bothner, and G. Steele, Coupling microwave photons to a mechanical resonator using quantum interference, Nature communications 10, 5359 (2019).
- S. Bose, K. Jacobs, and P. L. Knight, Preparation of nonclassical states in cavities with a moving mirror, Phys. Rev. A 56, 4175 (1997).
- A. Nunnenkamp, K. Børkje, and S. M. Girvin, Single-photon optomechanics, Phys. Rev. Lett. 107, 063602 (2011).
- P. Rabl, Photon blockade effect in optomechanical systems, Phys. Rev. Lett. 107, 063601 (2011).
- J.-Q. Liao and F. Nori, Photon blockade in quadratically coupled optomechanical systems, Phys. Rev. A 88, 023853 (2013).
- C. K. Law, Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation, Phys. Rev. A 51, 2537 (1995).
- See supplemental material.
- J. Goldstone, A. Salam, and S. Weinberg, Broken symmetries, Phys. Rev. 127, 965 (1962).
- X.-G. Wen, Quantum field theory of many-body systems: from the origin of sound to an origin of light and electrons (Oxford University Press, New York, 2004).
- S. Felicetti and A. Le Boité, Universal spectral features of ultrastrongly coupled systems, Phys. Rev. Lett. 124, 040404 (2020).
- We consider the resonant relationship between the cavity frequency and the atomic transition frequency. Moreover, using Hamiltonian Hopsubscript𝐻opH_{\text{op}}italic_H start_POSTSUBSCRIPT op end_POSTSUBSCRIPT in Eq. (10) instead of H𝐻Hitalic_H to describe the optomechanical system can also obtain the same conclusions.
- S. Savasta, O. Di Stefano, and F. Nori, Thomas–Reiche–Kuhn (TRK) sum rule for interacting photons, Nanophotonics 10, 465 (2020).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.