arXiv subjects
Publications and source records attributed to Sang Wook Kim.
A set of gauge invariants are identified for the gauge theory of quantum anholonomies, which comprise both the Berry phase and an exotic anholonomy in eigenspaces. We examine these invariants for hierarchical families of quantum circuits whose qubit size can be arbitrarily large. It is also found that a hierarchical family of quantum circuits generally involves an NP-complete problem.
We propose a coupled microdisk laser as a compact and tunable laser source for the generation of a coherent continuous wave THz radiation by photomixing. Using the Schrödinger-Bloch model including the nonlinear effect of active medium, we find single mode and two mode lasings depending on the pumping strength. We explain the transitions of lasing modes in terms of resonant modes which are the solutions of the Schrödinger-Bloch model without active medium and nonlinear interaction. In particular, a two mode lasing is shown to generate THz oscillating frequency originating from the light beating of two nearly degenerated resonant modes with different symmetries.
We have investigated the exceptional points (EPs) which are degeneracies of a non-Hermitian Hamiltonian, in the case that three modes are interacting with each other. Even though the parametric evolution of the modes cannot be uniquely determined when encircling more than two EPs once, we can recover the initial configuration of the modes by encircling two EPs three times or three EPs twice. We confirm our expectation by numerically calculating the modes of an open quantum system, two dielectric microdisks, and 3$\times$3 matrix model.
We study the origin of attracting phenomena in the ray dynamics of coupled optical microcavities. To this end we investigate a combined map that is composed of standard and linear map, and a selection rule that defines when which map has to be used. We find that this system shows attracting dynamics, leading exactly to a quasiattractor, due to collapse of phase space. For coupled dielectric disks, we derive the corresponding mapping based on a ray model with deterministic selection rule and study the quasiattractor obtained from it. We also discuss a generalized Poincaré surface of section at dielectric interfaces.
In this article we have investigated the effect of weak random disorder in the BCS-BEC crossover region. The disorder is included in the mean field formalism through NSR theory of superconducting fluctuations. A self consistent numerical solution of the coupled equations involving the superfluid gap parameter and density as a function of the disorder strength, albeit unaffected in the BCS phase, yields a depleted order parameter in the BEC regime and an interesting nonmonotonic behavior of the condensate fraction in the vicinity of the unitary region, and a gradual depletion thereafter, as the pairing interaction is continuously tuned across the BCS-BEC crossover. The unitary regime thus demonstrates a robust paradigm of superfluidity even when the disorder is introduced. To support the above feature and shed light on a lingering controversial issue, we have computed the behavior of the sound mode across the crossover that distinctly reveals a suppression of the sound velocity. We also find the Landau critical velocity that shows similar nonmonotonicity as that of the condensate fraction data, thereby supporting a stable superfluid scenario in the unitary limit.
The role of the third law of thermodynamics in the Szilard engine has been addressed. If the ground state is non-degenerate, the entropy production defined as the work extractable from the engine divided by temperature vanishes as temperature approaches zero due to the third law. The degenerate ground state induced by the symmetry or by accidence gives rise to non-zero entropy production at zero temperature associated with the residual entropy. Various physical situations such as the SZE consisting of bosons or fermions either with or without interaction have been investigated.
An adiabatic cycle of parameters in a quantum system can yield the quantum anholonomies, nontrivial evolution not just in phase of the states, but also in eigenvalues and eigenstates. Such exotic anholonomies imply that an adiabatic cycle rearranges eigenstates even without spectral degeneracy. We show that an arbitrarily large quantum circuit generated by recursive extension can also exhibit the eigenvalue and eigenspace anholonomies.
We derive the work performed in the Szilard engine (SZE) by using dissipative work formula of non-equilibrium thermodynamics developed in Kawai et al. Phys. Rev. Lett. 98, 080602 (2007). The work is described as the difference of probability distributions of measurement outcomes of the time forward and the backward process.
The Szilard engine (SZE) is the quintessence of Maxwell's demon, which can extract the work from a heat bath by utilizing information. We present the first complete quantum analysis of the SZE, and derive an analytic expression of the quantum-mechanical work performed by a quantum SZE containing an arbitrary number of molecules, where it is crucial to regard the process of insertion or removal of a wall as a legitimate thermodynamic process. We find that more (less) work can be extracted from the bosonic (fermionic) SZE due to the indistinguishability of identical particles.
We study the evolution of quantum eigenstates in the presence of level crossing under adiabatic cyclic change of environmental parameters. We find that exotic holonomies, indicated by exchange of the eigenstates after a single cyclic evolution, can arise from non-Abelian gauge potentials among non-degenerate levels. We illustrate our arguments with solvable two and three level models.
We present spectroscopic observation of an exceptional point or the transition point between diabatic crossing and avoided crossing of neighboring quasi-eigenmodes in a chaotic optical microcavity with a large size parameter. The transition to the avoided crossing was impeded until the degree of deformation exceeded a threshold deformation owing to the system's openness also enhanced by the shape deformation. As a result, a singular topology was observed around the exceptional point on the eigenfrequency surfaces, resulting in fundamental inconsistency in mode labeling.
We investigate two coupled microdisks with non-identical radii focusing on the parametric evolution of energy levels and the unidirectional far-field emission. We show that the evolution of energy levels is characterized by the avoided crossing intrinsically associated with the exceptional point or the non-Hermitian degeneracy. These spectral properties explain highly asymmetric near-field intensity pattern of the resonance mode. The observed unidirectional far-field emission is shown to be understood by considering the forbidden inter-disk coupling in the ray picture induced by the frustrated total internal reflection near the closest point between two disks when the inter-disk distance is small enough.
We experimentally studied evolution of quasi-eigenmodes as classical dynamics undergoing a transition from being regular to chaotic in open quantum billiards. In a deformation-variable microcavity we traced all high-Q cavity modes in a wide range of frequency as the cavity deformation increased. By employing an internal parameter we were able to obtain a mode-dynamics diagram at a given deformation, showing avoided crossings between different mode groups, and could directly observe the coupling strengths induced by ray chaos among encountering modes. We also show that the observed mode-dynamics diagrams reflect the underlying classical ray dynamics in the phase space.
An adiabatic change of a bound state along a closed circuit in the parameter space can induces holonomies not only in the phase of the state, but also in the associated eigenspace and eigenvalue. The former is the well-known Berry phase while the latter, namely the exotic holonomy, is found a decade ago and its origin has not been understood yet. By extending the parameter into the complex number, the correspondence of the exotic holonomies and the degeneracy of the non-Hermitian Hamiltonian, or the exceptional points, is revealed. We show that this explains all the known non-trivial characteristics of the exotic holonomies.
Quasi-bound states in an open system do in general not form an orthogonal and complete basis. It is, however, expected that the non-orthogonality is weak in the case of well-confined states except close to a so-called exceptional point in parameter space. We present numerical evidence showing that for passive optical microspiral cavities the parameter regime where the non-orthogonality is significant is rather broad. Here we observe almost-degenerate pairs of well-confined modes which are highly non-orthogonal. Using a non-Hermitian model Hamiltonian we demonstrate that this interesting phenomenon is related to the asymmetric scattering between clockwise and counterclockwise propagating waves in the spiral geometry. Numerical simulations of ray dynamics reveal a clear ray-wave correspondence.
We study a quasi-Floquet state of a $δ$-kicked rotor with absorbing boundaries focusing on the nature of the dynamical localization in open quantum systems. The localization lengths $ξ$ of lossy quasi-Floquet states located near the absorbing boundaries decrease as they approach the boundary while the corresponding decay rates $Γ$ are dramatically enhanced. We find the relation $ξ\sim Γ^{-1/2}$ and explain it based upon the finite time diffusion, which can also be applied to a random unitary operator model. We conjecture that this idea is valid for the system exhibiting both the diffusion in classical dynamics and the exponential localization in quantum mechanics.
Efficient control of spin squeezing in a two-component Bose-Einstein Condensate is studied by rapidly turning-off the external field at a time that maximal spin squeezing appears. We show that strong reduction of spin fluctuation can be maintained in a nearly fixed direction for a long time. We explain the underlying physics unambiguously, and present analytical expressions of the maximal-squeezing time.
We investigate the stimulated Raman adiabatic passage in two-color photoassociation for a atom-molecule Bose-Einstein condensate. By applying two time-varying Guassian laser pulses that fulfill generalized two-photon resonance condition, we obtain highly efficient atom-molecule conversion. The efficiency depends on the free-bound detuning and the delay time between the two pulses. By adjusting the parameters optimally, we achieve 92% conversion efficiency.