Collapse And Revival Research Articles

Exact quantum dynamics of XXZ central spin problems

We obtain analytically close forms of benchmark quantum dynamics of the collapse and revival (CR), reduced density matrix, Von Neumann entropy, and fidelity for the XXZ central spin problem. These quantities characterize the quantum decoherence and entanglement of the system with few to many bath spins, and for a short to infinitely long time evolution. For the homogeneous central spin problem, the effective magnetic field $B$, coupling constant $A$ and longitudinal interaction $\Delta$ significantly influence the time scales of the quantum dynamics of the central spin and the bath, providing a tunable resource for quantum metrology. Under the resonance condition $B=\Delta=A$, the location of the $m$-th revival peak in time reaches a simple relation $t_{r} \simeq\frac{\pi N}{A} m$ for a large $N$. For $\Delta =0$, $N\to \infty$ and a small polarization in the initial spin coherent state, our analytical result for the CR recovers the known expression found in the Jaynes-Cummings model, thus building up an exact dynamical connection between the central spin problems and the light-matter interacting systems in quantum nonlinear optics. In addition, the CR dynamics is robust to a moderate inhomogeneity of the coupling amplitudes, while disappearing at strong inhomogeneity.

Nonclassical Properties in Mesoscopic Josephson Junction with Excited Even and Odd Coherent States**The project supported by the Natural Science Foundation of Education Bureau of Jiangsu Province of China

Dynamic evolution of a mesoscopic Josephson junction (MJJ) interacting with excited even and odd coherent states is studied. It is shown that the supercurrent in MJJ exhibits both collapse and revival (CR) phenomenon and squeezing effect. It is also shown that the CR and squeezing of supercurrent are related to degree of excitation and average photon number.

Collapse and revival in Aharonov-Bohm electron interference experiment

It is shown that in the presence of even and odd coherent state field the collapse and revival (CR) phenomenon can occur in Aharonov-Bohm electron interference, which is closely related to the quantum fluctuation of the field. CR phenomenon reflects the effects of quantum noise of the field on the dynamic behaviour of electron interference. For coherent state field and number state field there is no CR to occur, which means that CR is due to both wave and particle aspects of the field.

Aharonov-Bohm-Type Electron Interference in a Two-Mode Squeezed Vacuum Field

Electron interference related to Aharonov-Bohm effect in the presence of the two-mode quantized radiation field is investigated. Characteristics of the temporal behavior of electron interference are discussed. It is shown that for the two-mode squeezed vacuum field the time evolution of the intensity of electron interference can exhibit very interesting periodic spontaneous collapse and revival (CR). In addition, the relation between CR and the quantum fluctuation in electron interference is also discussed.

Characteristics of Aharonov–Bohm Electron Interference in Two-Mode Squeezed Vacuum

Electron interference related to Aharonov–Bohm effect in the presence of the two-mode quantized radiation field is investigated. Characteristics of Shapiro steps, the visibility of the interference fringe and the temporal behavior of electron interference in correlated and uncorrelated two-mode radiation field are discussed. It is shown that for the correlated two-mode squeezed vacuum the integer Shapiro steps are obtained and the time evolution of the intensity of electron interference can exhibit very interesting periodic spontaneous collapse and revival (CR), while for the uncorrelated two-mode coherent state the fractional Shapiro steps are obtained and the CR phenomenon does not occur. In addition, the relation between CR and the quantum fluctuation in electron interference is also discussed.

Dynamic behaviour of electron interference in the two-mode SU(1,1) coherent state field

Aharonov-Bohm-type electron interference in the presence of the two-mode SU(1,1) coherent state(CS) field is investigated. The visibility of the time-averaged interference pattern is discussed for this state, and a comparison with classical cases is made. It is shown that the time evolution of the intensity of electron interference exhibits collapse and revival (CR) phenomenon for this state. The fluctuation in electron interference, and its relation to CR phenomenon are also discussed.

Aharonov-Bohm-type electron interference in the presence of one-mode SU(1,1) coherent state

Dynamic behaviour of Aharonov-Bohm-type electron interference in the presence of a nonclassical electromagnetic field is investigated. The visibility of the time-averaged interference pattern is discussed for SU(1,1) coherent state (CS) and a comparison with other states is made. It is shown that the dynamic behaviour of the electron interference exhibits collapse and revival (CR) phenomenon for SU(1,1) CS. It is also shown that CR phenomenon of electron interference is closely related to the fluctuation of a nonclassical electromagnetic field.

Dynamic behavior of the supercurrent in mesoscopic Josephson junctions in the presence of a nonclassical electromagnetic field

The dynamic behavior of the supercurrent in mesoscopic Josephson junctions interacting with various nonclassical electromagnetic fields (NEMF) is investigated. It is shown that for squeezed number states, squeezed states, and a superposition of two coherent states, the supercurrent exhibits a collapse and revival (CR) phenomenon that is well known in the context of quantum optics. For coherent states and number states, this phenomenon does not occur. This CR phenomenon, which is due to the granular nature of the field, is also absent if the field is considered classically. The dynamic behavior of the supercurrent fluctuation is also studied and it is found that, generally, when the fluctuation is large, the supercurrent exhibits collapses, and, when the fluctuation is small, the supercurrent exhibits revivals. Finally, the amplitude of current-voltage steps for various NEMF's are studied in some detail.

Collapse and revival of supercurrent in mesoscopic Josephson junction

The dynamic behaviour of the supercurrent in mesoscopic Josephson junctions in the presence of a dc voltage bias V 0 and quantized electromagnetic field is investigated. It is shown that the time evolution of the supercurrent exhibits collapse and revival (CR) for SU(1, 1) coherent state (CS), but for coherent states it does not exhibit such phenomenon.

Mesoscopic Josephson junctions in the presence of two-mode quantized electromagnetic field

Dynamic behavior of a mesoscopic Josephson junction in the presence of a two-mode quantized electromagnetic field is investigated. It is shown that the currentvoltage- step structures depend apparently on the two basic frequencies of the two-mode field. The voltage jumps are generally not equidistant. It is also shown that for the correlated two-mode squeezed state the time evolution of the supercurrent exhibits quantum collapse and revival(CR) phenomenon, while for the noncorrelated two-mode coherent state the phenomenon does not occur.