Myung-Joong Hwang

Quantum Phase Transition and Universal Dynamics in the Rabi Model.

We consider the Rabi Hamiltonian, which exhibits a quantum phase transition (QPT) despite consisting only of a single-mode cavity field and a two-level atom. We prove QPT by deriving an exact solution in the limit where the atomic transition frequency in the unit of the cavity frequency tends to infinity. The effect of a finite transition frequency is studied by analytically calculating finite-frequency scaling exponents as well as performing a numerically exact diagonalization. Going beyond this equilibrium QPT setting, we prove that the dynamics under slow quenches in the vicinity of the critical point is universal; that is, the dynamics is completely characterized by critical exponents. Our analysis demonstrates that the Kibble-Zurek mechanism can precisely predict the universal scaling of residual energy for a model without spatial degrees of freedom. Moreover, we find that the onset of the universal dynamics can be observed even with a finite transition frequency.

Probing the Dynamics of a Superradiant Quantum Phase Transition with a Single Trapped Ion

We demonstrate that the quantum phase transition (QPT) of the Rabi model and critical dynamics near the QPT can be probed in the setup of a single trapped ion. We first demonstrate that there exists equilibrium and nonequilibrium scaling functions of the Rabi model by finding a proper rescaling of the system parameters and observables, and show that those scaling functions are representative of the universality class to which the Rabi model belongs. We then propose a scheme that can faithfully realize the Rabi model in the limit of a large ratio of the effective atomic transition frequency to the oscillator frequency using a single trapped ion and, therefore, the QPT. It is demonstrated that the predicted universal functions can indeed be observed based on our scheme. Finally, the effects of realistic noise sources on probing the universal functions in experiments are examined.

Fate of photon blockade in the deep strong-coupling regime

We investigate the photon emission properties of the driven-dissipative Rabi model in the so-called ultrastrong- and deep strong-coupling regimes where the atom-cavity coupling rate

Excited-state quantum phase transition in the Rabi model

g

Variational study of a two-level system coupled to a harmonic oscillator in an ultrastrong-coupling regime

becomes comparable or larger than the cavity frequency

Quantum Phase Transition in the Finite Jaynes-Cummings Lattice Systems

{\ensuremath{\omega}}_{c}

Protected ultrastrong coupling regime of the two-photon quantum Rabi model with trapped ions

. By solving numerically the master equation in the dressed-state basis, we compute the output field correlation functions in the steady-state for a wide range of coupling rates. We find that, as the atom-cavity coupling strength increases, the system undergoes multiple transitions in the photon statistics. In particular, a first sharp antibunching-to-bunching transition, occurring at

Large-scale maximal entanglement and Majorana bound states in coupled circuit quantum electrodynamic systems

g\ensuremath{\sim}0.45{\ensuremath{\omega}}_{c}

Metastability in the driven-dissipative Rabi model

, leading to the breakdown of the photon blockade due to the counter-rotating terms, is shown to be the consequence of a parity shift in the energy spectrum. A subsequent revival of the photon blockade and the emergence of the quasicoherent statistics for even larger coupling rates are attributed to an interplay between the nonlinearity in the energy spectrum and the transition rates between the dressed states.

Pair tunneling and shot noise through a single molecule in a strong electron-phonon coupling regime

The Rabi model, a two-level atom coupled to a harmonic oscillator, can undergo a second-order quantum phase transition (QPT) [M.-J. Hwang et al., Phys. Rev. Lett. 115, 180404 (2015)]. Here we show that the Rabi QPT accompanies critical behavior in the higher-energy excited states, i.e., the excited-state QPT (ESQPT). We derive analytic expressions for the semiclassical density of states, which show a logarithmic divergence at a critical energy eigenvalue in the broken symmetry (superradiant) phase. Moreover, we find that the logarithmic singularities in the density of states lead to singularities in the relevant observables in the system such as photon number and atomic polarization. We corroborate our analytical semiclassical prediction of the ESQPT in the Rabi model with its numerically exact quantum mechanical solution.