Abstract
We study the thermodynamic properties of a system of two-level dipoles that are coupled ultrastrongly to a single cavity mode. By using exact numerical and approximate analytical methods, we evaluate the free energy of this system at arbitrary interaction strengths and discuss strong-coupling modifications of derivative quantities such as the specific heat or the electric susceptibility. From this analysis we identify the lowest-order cavity-induced corrections to those quantities in the collective ultrastrong coupling regime and show that for even stronger interactions the presence of a single cavity mode can strongly modify extensive thermodynamic quantities of a large ensemble of dipoles. In this non-perturbative coupling regime we also observe a significant shift of the ferroelectric phase transition temperature and a characteristic broadening and collapse of the black-body spectrum of the cavity mode. Apart from a purely fundamental interest, these general insights will be important for identifying potential applications of ultrastrong-coupling effects, for example, in the field of quantum chemistry or for realizing quantum thermal machines.
Highlights
The interplay between statistical physics and the theory of electromagnetic (EM) radiation played a very important role in the history of modern physics
Investigations of photon-photon correlations from thermal and coherent sources of light stood at the beginning of the field of quantum optics, and so on. In most of these and related examples the EM field can be treated as an independent subsystem, which thermalizes via weak interactions with the surrounding matter. This assumption breaks down in the so-called ultrastrong coupling (USC) regime [1, 2, 3], where the interaction energy can be comparable to the bare energy of the photons
Such conditions can be reached in solid-state [4, 5, 6, 7, 8, 9, 10] and molecular cavity QED experiments [11, 12, 13, 14, 15], where modifications of chemical reactions [16, 17] or phase transitions [18] have been observed and interpreted as vacuum-induced changes of thermodynamic potentials [19]
Summary
The interplay between statistical physics and the theory of electromagnetic (EM) radiation played a very important role in the history of modern physics. A prominent example in this respect is the superradiant phase transition of the Dicke model [45, 46, 47], which is often described as cavityinduced, but which can be understood as a regular ferroelectric instability in a system of strongly attractive dipoles [33, 41] In the past, these and other subtle issues have led to many controversies in this field and prevented a detailed understanding of the ground- and thermal states of USC light-matter systems so far. Since we are interested in both thermal und USC effects, we can restrict our discussion to cavity and circuit QED setups in the GHz to THz regime, where these effects are experimentally most relevant In this case the confined electromagnetic field can be represented by the fundamental mode of a lumped-element LC resonator [33, 51] with capacitance C and inductance L (see Fig. 1). The two states are separated by an energy ω0 and they are coupled via an electric transition dipole moment μ to the electric field
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