Optical signatures of quantum phase transitions in a light-matter system

Abstract

Information about quantum phase transitions in conventional condensed matter systems, must be sought by probing the matter system itself. By contrast, we show that mixed matter-light systems offer a distinct advantage in that the photon field carries clear signatures of the associated quantum critical phenomena. Having derived an accurate, size-consistent Hamiltonian for the photonic field in the well-known Dicke model, we predict striking behavior of the optical squeezing and photon statistics near the phase transition. The corresponding dynamics resemble those of a degenerate parametric amplifier. Our findings boost the motivation for exploring exotic quantum phase transition phenomena in atom-cavity, nanostructure-cavity, and nanostructure-photonic-band-gap systems.PACS numbers: 42.50.Fx, 32.80.t, 75.10.Nr There are several theoretical models which are currently attracting attention, based on the possible insights that they offer into the nature of Quantum Phase Transitions (QPTs). One of these is the Dicke model which was originally developed in quantum optics, together with its recent generalizations [1,2,3]. In practice, such exotic quantum phenomena can only be studied experimentally if the system's many-body quantum state can be probed in some way [4]. Unfortunately in condensed matter systems, such probing is typically indirect since one cannot 'see' many-body quantum spin states.Here we predict that in light-matter systems approximating to the Dicke model -such as atom-cavity and nanostructure-cavity systems [1, 2, 3, 4] -the statistical properties of the photon field offer direct and striking signatures of the quantum critical phenomena underlying a QPT. Our results are based on an accurate, size-consistent calculation of the statistical properties of the photon field in the Dicke model, and help motivate the exploration of such exotic quantum phenomena in atom-cavity, nanostructure-cavity, and nanostructure-photonic-band-gap systems [1,2,3,4]. In addition to the results themselves, our theoretical approach presents a number of distinct features over previous works [1, 2, 3, 4]: (1) we avoid using canonical perturbation schemes and projection methods, which can suffer from inconsistent size-dependencies as one approaches the thermodynamic limit [5]. Instead we adopt a similar renormalization-like scheme to Ref. [3], but take the opposite viewpoint by renormalizing the dynamics of the photon field as opposed to the matter system.(2) Our approach shows the direct connection between the Dicke model and a degenerate parametric optical amplifier. (3) In addition to explicitly reproducing the correct scaling near the critical point, we are able to show that striking signatures arise in a number of key statistical properties associated with the photon field. (4) We are able to show the optical manifestation of a quasi-integrable to quantum chaotic transition near the QPT.The Dicke model describes the interaction between a single-mode photon field and N non-interacting two-level systems [1,3]:whereare the c...

Robust quantum correlations in out-of-equilibrium matter–light systems

“…Experimental realizations of the DM have been presented in different settings, from proposed realizations in circuit quantum electrodynamics [7], to the recent very successful demonstrations of DM superradiance in various cold atom experiments [8]. While the light and matter properties in the equilibrium ground state are relatively well known [9][10][11][12][13], its fully quantum out-of-equilibrium critical behavior is just starting to be understood [14,15].In the DM, both the matter and field are known to act as mediators of an effective nonlinear self-interaction involving each other [10,13]. These nonlinear interactions produce interesting phenomena in both atomic and optical systems [16,17].…”

Quantum Terrorism: Collective Vulnerability of Global Quantum Systems

“…( 1), similar overall conclusions should follow from many variants of Eq. ( 1) due to an established universal dynamical scaling (29) and the fact that they typically generate similar types of phase diagrams, and hence have similar collective states in the static λ limit (49)(50)(51)(52). Indeed, we have already shown that for variants of Eq.…”

Circuit QED: superconducting qubits coupled to microwave photons

“…An array of resonators each containing a qubit that induces a Kerr nonlinearity will be a realization of the boson Hubbard model (Fisher et al, 1989) which exhibits both superfluid and Mott insulator phases. There is now a burgeoning interest in seeing 'quantum phase transitions of light' (Greentree et al, 2006;Illuminati, 2006;Hart-mann and Plenio, 2007;Jarrett et al, 2007;Rossini and Fazio, 2007;Angelakis et al, 2007;Hartmann et al, 2008;Makin et al, 2008;Aichhorn et al, 2008;Cho et al, 2008c;Cho et al, 2008a;Zhao et al, 2008;Na et al, 2008;Lei and Lee, 2008;Cho et al, 2008b;Ji et al, 2009;Hartmann et al, 2009;Grochol, 2009;Dalidovich and Kennett, 2009;Carusotto et al, 2009;Schmidt and Blatter, 2009;Koch and Le Hur, 2009;Lieb and Hartmann, 2010;Hartmann, 2010;Schmidt et al, 2010;Houck et al, 2012;Hayward et al, 2012;Nissen et al, 2012;Petrescu et al, 2012;Hwang and Choi, 2013;Schmidt and Koch, 2013). Since the transmon qubit is itself an anharmonic oscillator, one might imagine it would be easier to simply use a lattice of coupled transmons to realize the boson Hubbard model (with negative Kerr coefficient).…”