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arXiv:quant-ph/0609095 · Europhysics Letters (EPL)

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

Timothy Jarrett, Alexandra Olaya-Castro, Neil F. Johnson

Published Feb 1, 2007• 12 citations
arXivHTMLPDF

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. Possible realizations include atom-cavity, nanostructure-cavity, and nanostructure-photonic-band-gap systems.

DOI
10.1209/0295-5075/77/34001

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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. Possible realizations include atom-cavity, nanostructure-cavity, and nanostructure-photonic-band-gap systems.
We study the optical signatures of the quantum critical behaviour associated with the quantum phase transition exhibited by the Dicke model in the thermodynamic limit. We obtain an effective Hamiltonian for the radiation field, which resembles a degenerate parametric amplifier and which reproduces the Dicke's model critical behaviour. We identify the state of the radiation field in the sub-radiant and super-radiant phases, and show that the optical squeezing and photon statistics present striking behaviour in the vicinity of the phase transition. Our results are both of theoretical interest and of relevance to recent experimental proposals that hope to realize the quantum phase transition in the Dicke model.
The Dicke model describing an ensemble of two-state atoms interacting with a single quantized mode of the electromagnetic field (with omission of the ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{A}}^{2}$ term) exhibits a zero-temperature phase transition at a critical value of the dipole coupling strength. We propose a scheme based on multilevel atoms and cavity-mediated Raman transitions to realize an effective Dicke model operating in the phase transition regime. Optical light from the cavity carries signatures of the critical behavior, which is analyzed for the thermodynamic limit where the number of atoms is very large.
We study the coherent cooperative phenomena of the system composed of two interacting atomic ensembles in the thermodynamic limit. Remarkably, the system exhibits the Dicke-like quantum phase transition and entanglement behavior although the governing Hamiltonian is fundamentally different from the spin-boson Dicke Hamiltonian, offering the opportunity for investigating collective matter-light dynamics with pure matter waves. The model can be realized with two Bose-Einstein condensates or atomic ensembles trapped in two optical cavities coupled to each other. The interaction between the two separate samples is induced by virtual photon exchange.
We study the quantum phase transition of an N two-level system ensemble interacting with an optical degenerate parametric process, which can be described by the finite size Dicke Hamiltonian plus counter-rotating and quadratic field terms. Analytical closed forms of the critical coupling value and their corresponding separable ground states are derived in the weak and strong coupling regimes. The existence of bipartite entanglement between the two-level system ensemble and photon field as well as between ensemble components for moderate coupling is shown through numerical analysis. Given a finite size, our results also indicate the co-existence of squeezed fields and squeezed atomic ensembles.
As a hallmark of nonclassical light, squeezed light is of profound theoretical interest and holds broad practical promise for emerging quantum technologies. In this work, we investigate steady-state optical quadrature squeezing in the open quantum Rabi-Stark model by employing the quantum dressed master equation. Both numerically and analytically, we find that positive (negative) Stark coupling tends to enhance (suppress) the squeezing effect. The quadrature squeezing exhibits distinct signatures associated with both first- and second-order quantum phase transitions (QPTs). Notably, a sharp vanishing of squeezing is observed across the first-order QPT, suggesting its potential as a sensitive probe of such transitions. In the vicinity of the second-order QPT, we further demonstrate that the squeezing factor displays finite-size scaling behavior, indicating a promising route toward the realization of near-perfect squeezing. Moreover, we establish a quantitative criterion for the disruption of quantum criticality induced by thermal fluctuations, which may offer valuable guidance for future experiments. These findings contribute to a deep understanding of nonclassical light in light-matter interacting systems and provide useful insights for the design of strong optical squeezing states.
A phase transition describes the sudden change of state in a physical system, such as the transition between a fluid and a solid. Quantum gases provide the opportunity to establish a direct link between experiment and generic models which capture the underlying physics. A fundamental concept to describe the collective matter-light interaction is the Dicke model which has been predicted to show an intriguing quantum phase transition. Here we realize the Dicke quantum phase transition in an open system formed by a Bose-Einstein condensate coupled to an optical cavity, and observe the emergence of a self-organized supersolid phase. The phase transition is driven by infinitely long-ranged interactions between the condensed atoms. These are induced by two-photon processes involving the cavity mode and a pump field. We show that the phase transition is described by the Dicke Hamiltonian, including counter-rotating coupling terms, and that the supersolid phase is associated with a spontaneously broken spatial symmetry. The boundary of the phase transition is mapped out in quantitative agreement with the Dicke model. The work opens the field of quantum gases with long-ranged interactions, and provides access to novel quantum phases.