On the superradiant phase transition for molecules in a quantized radiation field: the dicke maser model

Hepp, K.; Lieb, Élliott H.

doi:10.1016/0003-4916(73)90039-0

Cited by 1,013 publications

(920 citation statements)

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“…inhomogeneous broadening) and coupling strengths. It is one of the central models of quantum optics, describing for example lasing [30], equilibrium superradiance [31], and dynamical superradiance [32]. It can be viewed as a generalization of the BCS Hamiltonian to the strong-coupling regime, as is apparent on rewriting the spin operators in terms of two species of fermions.…”

Section: Background and Basic Modelmentioning

confidence: 99%

The new physics of non-equilibrium condensates: insights from classical dynamics

Eastham¹

2007

J. Phys.: Condens. Matter

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Abstract. We discuss the dynamics of classical Dicke-type models, aiming to clarify the mechanisms by which coherent states could develop in potentially non-equilibrium systems such as semiconductor microcavities.We present simulations of an undamped model which show spontaneous coherent states with persistent oscillations in the magnitude of the order parameter. These states are generalisations of superradiant ringing to the case of inhomogeneous broadening. They correspond to the persistent gap oscillations proposed in fermionic atomic condensates, and arise from a variety of initial conditions. We show that introducing randomness into the couplings can suppress the oscillations, leading to a limiting dynamics with a time-independent order parameter. This demonstrates that non-equilibrium generalisations of polariton condensates can be created even without dissipation. We explain the dynamical origins of the coherence in terms of instabilities of the normal state, and consider how it can additionally develop through scattering and dissipation.

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Section: Background and Basic Modelmentioning

confidence: 99%

The new physics of non-equilibrium condensates: insights from classical dynamics

Eastham¹

2007

J. Phys.: Condens. Matter

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“…Superconducting qubits 7,8 have allowed the realization of strong 9,10 and ultrastrong 11-13 coupling between artificial atoms and cavities. If the coupling strength g becomes as large as the atomic and cavity frequencies (∆ and ω o , respectively), the energy eigenstates including the ground state are predicted to be highly entangled 14 . There has been an ongoing debate 15-17 over whether it is fundamentally possible to realize this regime in realistic physical systems.…”

mentioning

confidence: 99%

“…Superconducting qubits 7,8 have allowed the realization of strong 9,10 and ultrastrong [11][12][13] coupling between artificial atoms and cavities. If the coupling strength g becomes as large as the atomic and cavity frequencies (∆ and ω o , respectively), the energy eigenstates including the ground state are predicted to be highly entangled 14 . There has been an ongoing debate 15 We begin by describing the Hamiltonian of each component in the qubit-oscillator circuit, which comprises a superconducting flux qubit and an LC oscillator inductively coupled to each other by sharing a tunable inductance L c , as shown in the circuit diagram in Fig.…”

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confidence: 99%

Superconducting qubit–oscillator circuit beyond the ultrastrong-coupling regime

et al. 2016

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The interaction between an atom and the electromagnetic field inside a cavity 1-6 has played a crucial role in developing our understanding of light-matter interaction, and is central to various quantum technologies, including lasers and many quantum computing architectures. Superconducting qubits 7,8 have allowed the realization of strong 9,10 and ultrastrong 11-13 coupling between artificial atoms and cavities. If the coupling strength g becomes as large as the atomic and cavity frequencies (∆ and ω o , respectively), the energy eigenstates including the ground state are predicted to be highly entangled 14 . There has been an ongoing debate 15-17 over whether it is fundamentally possible to realize this regime in realistic physical systems. By inductively coupling a flux qubit and an LC oscillator via Josephson junctions, we have realized circuits with g/ω o ranging from 0.72 to 1.34 and g/∆ 1. Using spectroscopy measurements, we have observed unconventional transition spectra that are characteristic of this new regime. Our results provide a basis for ground-state-based entangled pair generation and open a new direction of research on strongly correlated light-matter states in circuit quantum electrodynamics.We begin by describing the Hamiltonian of each component in the qubit-oscillator circuit, which comprises a superconducting flux qubit and an LC oscillator inductively coupled to each other by sharing a tunable inductance L c , as shown in the circuit diagram in Fig. 1a.The Hamiltonian of the flux qubit can be written in the basis of two states with persistent currents flowing in opposite directions around the qubit loop 18 , |L q and |R q , as H q = − (∆σ x + εσ z )/2, where ∆ and ε = 2I p 0 (n φq − n φq0 ) are the tunnel splitting and the energy bias between |L q and |R q , I p is the maximum persistent current, and σ x, z are Pauli matrices. Here, n φq is the normalized flux bias through the qubit loop in units of the superconducting flux quantum, 0 = h/2e, and n φq0 = 0.5 + k q , where k q is the integer that minimizes |n φq − n φq0 |. The macroscopic nature of the persistent-current states enables strong coupling to other circuit elements. Another important feature of the flux qubit is its strong anharmonicity: the two lowest energy levels are well isolated from the higher levels.The Hamiltonian of the LC oscillator can be written asC is the resonance frequency, L 0 is the inductance of the superconducting lead, L qc ( L c ) is the inductance across the qubit and coupler (see Supplementary Section 2), C is the capacitance, andâ (â † ) is the oscillator's annihilation (creation) operator. Figure 1b shows a laser microscope image of the lumped-element LC oscillator, where L 0 is designed to be as small as possible to maximize the zeropoint fluctuations in the currentand hence achieve strong coupling to the flux qubit, while C is adjusted so as to achieve a desired value of ω o . The freedom of choosing L 0 for large I zpf is one of the advantages of lumped-element LC oscillators over coplanar-waveguide ...

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“…The average BP γ 1 /N is equal to π at λ < 1 and increases abruptly at discontinuous "critical" points when λ > 1. Note that the plateau is formed clearly for N = 1, 2, 4 , the width of the plateau becomes narrower and narrower with the increasing N , which are quite different from the phenomenon of the quantum phase transition in the full DM [7,8,9]. A clear picture of the instability in the ground state of the RWA DM is given in terms of the BP with N = 64 atoms shown in the inset of Fig.…”

Section: Ground State Propertymentioning

confidence: 87%

“…It has been attracted considerable attentions recently, mainly due to the fact that the Dicke model is closely related to many recent interesting fields in quantum optics and condensed matter physics, such as the superradiant behavior by an ensemble of quantum dots [2] and Bose-Einstein condensates [3], coupled arrays of optical cavities used to simulate and study the behavior of strongly correlated systems [4], and superconducting charge qubits [5,6]. It is known from the previous studies [7,8,9] that the full DM undergoes the second-order quantum phase transition [10].…”

Section: Introductionmentioning

confidence: 99%