Metastable Quantum Phase Transitions in a One-Dimensional Bose Gas

This is a chapter for a book. The first paragraph of this chapter is as follows: "Ultracold quantum gases offer a wonderful playground for quantum many body physics, as experimental systems are widely controllable, both statically and dynamically. One such system is the one-dimensional (1D) Bose gas on a ring. In this system binary contact interactions between the constituent bosonic atoms, usually alkali metals, can be controlled in both sign and magnitude; a recent experiment has tuned interactions over seven orders of magnitude, using an atom-molecule resonance called a Feshbach resonance. Thus one can directly realize the Lieb-Liniger Hamiltonian, from the weakly- to the strongly-interacting regime. At the same time there are a number of experiments utilizing ring traps. The ring geometry affords us the opportunity to study topological properties of this system as well; one of the main properties of a superfluid is the quantized circulation in which the average angular momentum per particle, L/N, is quantized under rotation. Thus we focus on a tunable 1D Bose system for which the main control parameters are interaction and rotation. We will show that there is a critical boundary in the interaction-rotation control-parameter plane over which the topological properties of the system change. This is the basis of our concept of \textit{metastable quantum phase transitions} (QPTs). Moreover, we will show that the finite domain of the ring is necessary for the QPT to occur at all because the zero-point kinetic pressure can induce QPTs, i.e., the system must be finite; we thus seek to generalize the concept of QPTs to inherently finite, mesoscopic or nanoscopic systems."Comment: 29 pages, 12 figures, book will appear later this year; v2 is in improved format and includes small corrections for final versio

Resonant tunneling and Fano resonance in quantum dots with electron-phonon interaction

We theoretically study the resonant tunneling and Fano resonance in quantum dots with electron-phonon (e-ph) interaction. We examine the bias-voltage ($V$) dependence of the decoherence, using Keldysh Green function method and perturbation with respect to the e-ph interaction. With optical phonons of energy $\omega_0$, only the elastic process takes place when $eV<\omega_0$, in which electrons emit and absorb phonons virtually. The process suppresses the resonant amplitude. When $eV>\omega_0$, the inelastic process is possible which is accompanied by real emission of phonons. It results in the dephasing and broadens the resonant width. The bias-voltage dependence of the decoherence cannot be obtained by the canonical transformation method to consider the e-ph interaction if its effect on the tunnel coupling is neglected. With acoustic phonons, the asymmetric shape of the Fano resonance grows like a symmetric one as the bias voltage increases, in qualitative accordance with experimental results.Comment: 28 pages, 11 figure

Hermitian conjugate measurement

We propose a new class of probabilistic reversing operations on the state of a system that was disturbed by a weak measurement. It can approximately recover the original state from the disturbed state especially with an additional information gain using the Hermitian conjugate of the measurement operator. We illustrate the general scheme by considering a quantum measurement consisting of spin systems with an experimentally feasible interaction and show that the reversing operation simultaneously increases both the fidelity to the original state and the information gain with such a high probability of success that their average values increase simultaneously.Comment: 26 pages, 4 figures; a paragraph is added in the introductio

Topological Winding and Unwinding in Metastable Bose-Einstein Condensates

Topological winding and unwinding in a quasi-one-dimensional metastable Bose-Einstein condensate are shown to be manipulated by changing the strength of interaction or the frequency of rotation. Exact diagonalization analysis reveals that quasidegenerate states emerge spontaneously near the transition point, allowing a smooth crossover between topologically distinct states. On a mean-field level, the transition is accompanied by formation of grey solitons, or density notches, which serve as an experimental signature of this phenomenon.Comment: 4 pages, 3 figure

Reversible quantum measurement with arbitrary spins

We propose a physically reversible quantum measurement of an arbitrary spin-s system using a spin-j probe via an Ising interaction. In the case of a spin-1/2 system (s=1/2), we explicitly construct a reversing measurement and evaluate the degree of reversibility in terms of fidelity. The recovery of the measured state is pronounced when the probe has a high spin (j>1/2), because the fidelity changes drastically during the reversible measurement and the reversing measurement. We also show that the reversing measurement scheme for a spin-1/2 system can serve as an experimentally feasible approximate reversing measurement for a high-spin system (s>1/2). If the interaction is sufficiently weak, the reversing measurement can recover a cat state almost deterministically in spite of there being a large fidelity change.Comment: 35 pages, 11 figures, Sec. 3.2 is adde

Many body effects in finite metallic carbon nanotubes

The non homogeneity of the charge distribution in a carbon nanotube leads to the formation of an excitonic resonance, in a similar way to the one observed in X-ray absorption in metals. As a result, a positive anomaly at low bias appears in the tunnelling density of states. This effect depends on the screening of the electron--electron interactions by metallic gates, and it modifies the coupling of the nanotube to normal and superconducting electrodes.Comment: 5 page

Phonon Spectroscopy by Electric Measurements of Coupled Quantum Dots

We propose phonon spectroscopy by electric measurements of the low-temperature conductance of coupled-quantum dots, specifically employing dephasing of the quantum electronic transport by the phonons. The setup we consider consists of a T-shaped double-quantum-dot (DQD) system in which only one of the dots (dot 1) is connected to external leads and the other (dot 2) is coupled solely to the first one. For noninteracting electrons, the differential conductance of such a system vanishes at a voltage located in-between the energies of the bonding and the anti-bonding states, due to destructive interference. When electron-phonon (e-ph) on the DQD is invoked, we find that, at low temperatures, phonon emission taking place on dot 1 does not affect the interference, while phonon emission from dot 2 suppresses it. The amount of this suppression, as a function of the bias voltage, follows the effective e-ph coupling reflecting the phonon density of states and can be used for phonon spectroscopy.Comment: 9 pages, 6 figure