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arXiv:cond-mat/0209627

Thermodynamic QED Coherence in Condensed Matter: Microscopic Basis of Thermal Superradiance

Sivasubramanian, S., A. Widom, Yogendra Narain Srivastava

Published Sep 26, 2002• 0 citations
arXivHTMLPDF

Abstract

Electromagnetic superradiant field coherence exists in a condensed matter system if the electromagnetic field oscillators undergo a mean displacement. Transitions into thermal states with ordered superradiant phases have been shown to theoretically exist in Dicke-Preparata models. The theoretical validity of these models for condensed matter has been called into question due to non-relativistic diamagnetic terms in the electronic Hamiltonian. The microscopic bases of Dicke-Preparata thermal superradiance for realistic macroscopic systems are explored in this work. The impossibility of diaelectric correlations in condensed matter systems (via the Landau-Lifshitz theorem) provides a strong theoretical basis for understanding the physical reality of condensed matter thermodynamic superradiant phases.

DOI
10.48550/arxiv.cond-mat/0209627

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Electromagnetic superradiant field coherence exists in a condensed matter system if the electromagnetic field oscillators undergo a mean displacement. Transitions into thermal states with ordered superradiant phases have been shown to theoretically exist in Dicke-Preparata models. The theoretical validity of these models for condensed matter has been called into question due to non-relativistic diamagnetic terms in the electronic Hamiltonian. The microscopic bases of Dicke-Preparata thermal superradiance for realistic macroscopic systems are explored in this work. The impossibility of diaelectric correlations in condensed matter systems (via the Landau-Lifshitz theorem) provides a strong theoretical basis for understanding the physical reality of condensed matter thermodynamic superradiant phases.
In this doctoral thesis, the thermodynamic phases und phase transitions of a generalised Dicke model are studied and characterised. Both, finite and vanishing temperatures are considered. The Dicke model of quantum optics describes collective phenomena which occur when light interacts with a many-atom system. In the thermodynamic limit, a so-called Hepp–Lieb superradiant phase transition sets in. A superradiant phase develops for low temperatures or strong coupling between light and atoms, which is characterised by a macroscopic excitation of the light field and a spontaneous, collective polarisation of the atoms. This thesis discusses a generalised version of the Dicke model, which is described by a quantum mechanical system consisting of three-level atoms in Lambda-configuration and two modes of a resonator. By means of the Holstein–Primakoff transformation, the Hamiltonian of this system is written in terms of four interacting, non-linear oscillators, which can be linearised in the thermodynamic limit, yielding the ground-state energy as well as the low-energy excitations. The phase diagram consisting of two superradiant phases separated by continuous and first-order phase transitions is derived. In order to clarify the question whether or not the superradiant phase transition of this generalised Dicke model can be observed experimentally for real atoms, the significance of the diamagnetic term is discussed. In contrast to the original Dicke model, superradiant phase transitions are possible in principle. This is due to the first-order phase transitions. In addition, a no-go theorem for continuous superradiant phase transitions is presented. The argument is based on the Thomas–Reiche–Kuhn sum rule. Last, we study the superradiant phase transition of the generalised Dicke model at finite temperatures. Therefore, the partition sum is computed and analysed in the thermodynamic limit using Laplace’s method. At finite temperatures, the properties of the phase diagram and phases remain. However, here all phase transitions are of first order.
The atom - electromagnetic field interaction is studied in the Dicke model, wherein a single field mode is interacting with a collection of two level atoms at thermal equilibrium. It is found that in the superradiant phase of the system, wherein the Bose-Einstein condensation of photons takes place, the notion of photon as an elementary electromagnetic excitation ceases to exist. The phase and intensity excitations of the condensate are found to be the true excitations of electromagnetic field. It is found that in this phase, the atom interacts with these excitations in a distinct coherent transition process, apart from the known stimulated emission/absorption and spontaneous emission processes. In the coherent transition it is found that while the atomic state changes in course of the transition process, the state of electromagnetic field remains unaffected. It is found that the transition probability of such coherent transition process is macroscopically large compared to other stimulated emission/absorption and spontaneous emission processes.
Dicke superrandiance is a cooperative phenomenon which arises from the collective coupling of an ensemble of atoms to the electromagnetic radiation. Here we discuss the quantifying of quantum coherence for the Dicke model of superradiance in the mean-field approximation. We found the single-atom l1{l}_{1}l1​ norm of coherence is given by the square root of the normalized average intensity of radiation emitted by the superradiant system. This validates quantum coherence as a useful figure of merit towards the understanding of superradiance phenomenon in the mean-field approach. In particular, this result suggests probing the single-atom coherence through the radiation intensity in superradiant systems, which might be useful in experimental realizations where is unfeasible to address atoms individually. Furthermore, given the nonlinear unitary dynamics of the time-dependent single-atom state that effectively describes the system of NNN atoms, we analyze the quantum speed limit time and its interplay with the l1{l}_{1}l1​ norm of coherence. We verify the quantum coherence speeds up the evolution of the superradiant system, i.e., the more coherence stored on the single-atom state, the faster the evolution. These findings unveil the role played by quantum coherence in superradiant systems, which in turn could be of interest for communities of both condensed matter physics and quantum optics.
In order to examine whether or not the quantum phase transition of Dicke type exists in realistic systems, we revisit the model setup of the superconducting circuit QED from a microscopic many-body perspective based on the BCS theory with pseudo-spin presentation. By deriving the Dicke model with the correct charging terms from the minimum coupling principle, it is shown that the circuit QED system can exhibit superradiant quantum phase transition in the limit N\rightarrow\infty. The critical point could be reached at easiness by adjusting the extra parameters, the ratio of Josephson capacitance C_{J} to gate capacitance C_{g}, as well as the conventional one, the ratio of Josephson energy E_{J} to charging energy E_{C}.
The thermodynamics and electrodynamics of the superradiant phase are analyzed on the basis of the Emeljanov-Klimontovich model by means of a mean field approach and random phase approximation. The model considers infinite modes of radiation field. The superradiant phase is characterized by a static and homogeneous Bose condensation of the transverse collective mode with zero wave vector. The thermodynamic quantities and the dispersion relations for the collective mode are obtained in closed forms. While the thermodynamic properties of the present model are the same as those of the Dicke model, the electrodynamics differs in form from the latter. A softening of the lower branch of the collective mode behaves as (T-Tc)1/2 for T>Tc, whereas for T≪Tc it obeys a law Tc-T or (Tc-T)1/2 according to the different regions of temperature and the polarizations. A light velocity is renormalized with an anisotropic constant.