We investigate the role of phase transitions into the spontaneous-emission rate of a single quantum emitter embedded in a critical medium. Using a Landau-Ginzburg approach, we find that in the broken symmetry phase, the emission rate is reduced, or even suppressed, due to the photon mass generated by the Higgs mechanism. Remarkably, its sensitivity to the critical exponents of the phase transition allows for an optical determination of universality classes. When applied to the cases of superconductivity and superfluidity, we show that the Purcell effect also provides valuable information on spectroscopic and thermodynamic quantities, such as the size of the superconducting gap and the discontinuity in the specific heat at the transition. By unveiling that a deeper connection between the Purcell effect and phase transitions exists, we demonstrate that the former is an efficient optical probe of distinct critical phenomena and their associated observables.
We investigate the role of phase transitions into the spontaneous-emission rate of a single quantum emitter embedded in a critical medium. Using a Landau-Ginzburg approach, we find that in the broken symmetry phase, the emission rate is reduced, or even suppressed, due to the photon mass generated by the Higgs mechanism. Remarkably, its sensitivity to the critical exponents of the phase transition allows for an optical determination of universality classes. When applied to the cases of superconductivity and superfluidity, we show that the Purcell effect also provides valuable information on spectroscopic and thermodynamic quantities, such as the size of the superconducting gap and the discontinuity in the specific heat at the transition. By unveiling that a deeper connection between the Purcell effect and phase transitions exists, we demonstrate that the former is an efficient optical probe of distinct critical phenomena and their associated observables.
In this study, we present theoretical investigations of phase transitions and critical phenomena in materials through the lens of second-order Ginzburg-Landau theory, in conjunction with considerations of symmetry groups and thermal fluctuations. By addressing the residual effects after a renormalization process, a small number of macroscopic degrees of freedom can effectively replace the infinite number of microscopic degrees of freedom, emphasizing the significant role of dimensionality and the intrinsic characteristics of the system in understanding and analyzing transitions. We highlight several non-universal characteristics of continuous phase transitions near the transition temperature, including the non-monotonic relationship between the critical temperature and dimensionality, as well as the enhancement or disappearance of the specific heat jump in complex superconductors. While the resulting expressions for thermodynamic quantities are complex for one-dimensional systems, obeying Mermin-Wagner's theorem, they are considerably simplified for two-dimensional and three-dimensional systems.
Superfluids and superconductors can be either fully gapped or gapless with nodal structures in momentum space. Both the gapped and nodal phases can be topologically protected and possess nontrivial topological invariants. Topological quantum phase transitions exist at zero temperature between different gapped phases or between gapped and nodal phases. These phase transitions can be driven by chemical potential and/or spin exchange fields. The two phases separated by the phase transition can have the same local order but differ in global topology. Thus, these topological quantum phase transitions cannot be described by the Landau paradigm of symmetry breaking. Although some aspects of these transitions, such as the change of topological invariants and gapless boundary states, have been discussed before, a complete theory of these transitions has yet to be developed. In this dissertation, we construct effective field theories to study the universality and thermodynamic signatures of these transitions. We find four different universality classes in superfluids and superconductors. Certain thermodynamic quantities, such as compressibility or spin susceptibility, change non-analytically across the transitions. For certain time-reversal symmetry breaking fields that lead to bulk phase transitions, there also exist topological phase transitions on the surface. All the topological phase transitions studied in this dissertation only exist at zero temperature. At finite temperature, different states are connected by smooth crossovers. There exists a quantum critical region at finite temperature near the quantum critical point (QCP). In this quantum critical region, thermodynamic quantities have universal scaling dependence on temperature dictated by the universality class of the QCP. We argue that these scaling properties can be used to probe and differentiate these QCPs. These bulk and surface topological quantum phase transitions are discussed in various concrete models, such as chiral and time-reversal invariant p-wave superfluids, topological superconductors of emergent Dirac fermions, and topological superconducting model of CuₓBi₂Se₃.
Classical and quantum criticality In most cases the phases of quantum field theories, in particular those of interest in condensed matter physics, can be described in terms of the behavior of local observables, such as order parameters or currents that transform properly under the symmetries of the theory. Quantum and thermal phase transitions are characterized by the behavior of these observables as a function of temperature and of the coupling constants of the theory. The phase transitions themselves, quantum or thermal, are classified into universality classes, which are represented by the critical exponents which specify the scaling laws of the expectation values of the observables. Historically, the development of this approach to critical behavior goes back to the Landau theory of critical behavior. It acquired its most complete form with the development of the renormalization group (RG) in the late 1960s and early 1970s. It is the centerpiece of Wilson’s approach to quantum field theory, in which all local quantum field theories are defined by the scaling regime of a physical system near a continuous phase transition. From this point of view there is no fundamental difference between classical (or thermal) phase transitions, which are described by the theory of classical critical behavior, and quantum phase transitions. For example, the expectation value of a local order parameter M as the thermal phase transition is approached from below behaves as M ~ (Tc − T) β . Here T c is the critical temperature and β is a critical exponent that depends on the universality class of the thermal phase transition and on the dimensionality of space. While quantum mechanics can play a key role in the existence of the ordered phase, e.g. superfluidity and superconductivity are macroscopic manifestations of essentially quantum-mechanical phenomena, the thermal transition itself is governed entirely by classical statistical mechanics, and quantum mechanics plays a role in setting the value of non-universal quantities such as the critical temperature, etc. On the other hand, in the case of a quantum phase transition, the order parameter M has a similar scaling behavior as a function of the coupling constant, M~(gc−g)β˜, where g is the coupling constant, g c is the critical coupling constant, and β˜ is a critical exponent that depends on the universality class of the quantum phase transition. Here we assume that M has a non-vanishing expectation value only for g < g c .
Spontaneous emission into micro- or nano-scale structures can be enhanced or inhibited by engineering the local density of optical states using closed quantum cavities. When electromagnetic fields are confined within small mode volumes of a high-Q symmetrical closed quantum cavity, the Purcell effect significantly accelerates the natural spontaneous emission. Due to the statistical nature of spontaneous emission, the emitted fields do not have a well-defined phase; consequently, the emission is incoherent and lacks directional control. The situation becomes more complicated in multi-mode cavities, as selecting a specific mode in a particular direction requires precise detuning between the emitter transition frequency and the cavity mode frequency to ensure strong coupling. In single-mode cavities, only the dominant mode can resonate, and only in a specific direction; thus, an appropriate transition frequency range can be easily determined. Such cavities allow for greater manipulation of the local electromagnetic density of states, facilitating effective control of the direction of spontaneous emission. This property is essential for creating efficient single-photon sources, photonic circuits, and on-chip quantum information.
Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian. This mechanism gives rise to massless Nambu-Goldstone modes and massive Anderson-Higgs modes. These modes provide a fundamental understanding of matter in the Universe and appear as collective phase or amplitude excitations of an order parameter in a many-body system. The amplitude excitation plays a crucial role in determining the critical exponents governing universal nonequilibrium dynamics in the Kibble-Zurek mechanism (KZM). Here, we characterize the amplitude excitations in a spin-1 condensate and measure the energy gap for different phases of the quantum phase transition. At the quantum critical point of the transition, finite-size effects lead to a nonzero gap. Our measurements are consistent with this prediction, and furthermore, we demonstrate an adiabatic quench through the phase transition, which is forbidden at the mean field level. This work paves the way toward generating entanglement through an adiabatic phase transition.
The condensation of photons in a dye-filled optical microcavity represents a landmark achievement in macroscopic quantum phenomena, bridging quantum optics and statistical mechanics. While ordinary Bose-Einstein condensation (BEC) of massive particles is governed by well-established critical exponents, photon condensation occurs in an open, dissipative system where thermalization is mediated through repeated absorption and re-emission cycles by dye molecules. In this paper, we systematically investigate whether photon condensation exhibits independent critical exponents. We define the scaling of the condensed photon density as n_gamma proportional to |T - T_c|^(beta_gamma) and examine whether the critical exponent beta_gamma deviates significantly from the classical values associated with standard three-dimensional or trapped two-dimensional Bose systems. Through a rigorous theoretical formulation based on master equations, grand canonical statistical mechanics, and renormalization group techniques, we explore the universal properties of this light-matter phase transition. Establishing a distinct set of critical exponents for photon condensation could lay the foundational stone for a new universal class of non-equilibrium quantum phase transitions, offering profound implications for fundamental physics and advanced quantum technologies.