Amplified thermal state: Properties and decoherence

In this paper, we introduce the amplified thermal state (ATS) by operating [Formula: see text] on the thermal state (TS). Here, [Formula: see text] is the amplification factor and [Formula: see text] is the photon number operator. We study its properties, such as light intensity, signal-to-noise ratio (SNR), Fock matrix elements and Wigner function. In addition, we study its decoherence in photon-loss channel by analyzing evolution of all above properties. All considered properties are derived analytically and simulated numerically. Compared with the original TS, the amplification can enhance light intensity and SNR, remain the mixed character, and exhibit non-Gaussianity. While the decoherence will weaken light intensity and SNR, remain the mixed character, and return to Gaussian state.

Fractional Langevin type equations for white noise distributions

In this paper, by applying the intertwining properties, we introduce the fractional powers of the number operator perturbed by generalized Gross Laplacians (infinite dimensional Laplacians), which are special types of the infinitesimal generators of generalized Mehler semigroups. By applying the intertwining properties and semigroup approach, we study the Langevin type equations associated with the infinite dimensional Laplacians and with white noise distributions as forcing terms. Then we investigate the unique solution of the fractional Langevin type equations associated with the Riemann-Liouville and Caputo time fractional derivatives, and the fractional power of the infinite dimensional Laplacians, for which we apply the intertwining properties again. For our purpose, we discuss the fractional integrals and fractional derivatives of white noise distribution valued functions.

Quantum Fluctuations in the Effective Relational GFT Cosmology

We analyze the size and evolution of quantum fluctuations of cosmologically relevant geometric observables, in the context of the effective relational cosmological dynamics of GFT models of quantum gravity. We consider the fluctuations of the matter clock observables, to test the validity of the relational evolution picture itself. Next, we compute quantum fluctuations of the universe volume and of other operators characterizing its evolution (number operator for the fundamental GFT quanta, effective Hamiltonian and scalar field momentum). In particular, we focus on the late (clock) time regime, where the dynamics is compatible with a flat FRW universe, and on the very early phase near the quantum bounce produced by the fundamental quantum gravity dynamics.

The anti-Jaynes-Cummings model is solvable : quantum Rabi model in rotating and counter-rotating frames ; following the experiments

This article is a response to the continued assumption, cited even in reports and reviews of recent experimental breakthroughs and advances in theoretical methods, that the antiJaynes-Cummings (AJC)interaction is an intractable energy non-conserving component of the quantum Rabi model (QRM). We present three key features of QRM dynamics : (a) the AJC interaction component has a conserved excitation number operator and is exactly solvable (b) QRM dynamical space consists of a rotating frame (RF) dominated by an exactly solved Jaynes-Cummings (JC) interaction specied by a conserved JC excitation number operator which generates the U(1) symmetry of RF and a correlated counter-rotating frame (CRF) dominated by an exactly solved antiJaynes-Cummings (AJC) interaction specied by a conserved AJC excitation number operator which generates the U(1) symmetry of CRF (c) for QRM dynamical evolution in RF, the initial atom-eld state je0i is an eigenstate of the effective AJC Hamiltonian HAJC, while the effective JC Hamiltonian HJC drives this initial state je0i into a time evolving entangled state, and, in a corresponding process for QRM dynamical evolution in CRF, the initial atom-eld state jg0i is an eigenstate of the effective JC Hamiltonian, while the effective AJC Hamiltonian drives this initial state jg0i into a time evolving entangled state, thus addressing one of the long-standing challenges of theoretical and experimental QRM dynamics; consistent generalizations of the initial states je0i , jg0i to corresponding n 0 entangled eigenstates j+en i , j 􀀀g ni of the AJC in RF and JC in CRF, respectively, provides general dynamical evolution of QRM characterized by collapses and revivals in the time evolution of the atomic, eld mode, JC and AJC excitation numbers for large initial photon numbers ; the JC and AJC excitation numbers are conserved in the respective frames RF, CRF, but each evolves with time in the alternate frame.

Generating new nonclassical state by repeatedly operating number operator on coherent state

In this paper, using the principle of quantum state superposition, we report a nonclassical quantum state which is constructed by repeatedly operating the number operator on the coherent state. Nonclassical effects of this state are discussed by photon-number distribution, sub-Poissonian statistics, anti-bunching and negativity of Wigner function and squeezing effect. Our work provides an important nonclassical resource, which may be used in quantum communication and quantum optics.

Signal characters and non-classical properties of quadratically amplified squeezed vacuum

Based on the squeezed vacuum (SV) and the quadratic function of the photon number operator, we introduce the quadratically amplified squeezed vacuum (QASV) in this paper. We study the intensity, noise, squeezing effect, antibunching effect, and Wigner function of the QASVs. Compared with the SV, the QASVs have distinctive signal characters and possess peculiar non-classical properties in the proper range of interaction parameters.

Essence and Definition by Abstraction

We may define words. We may also define the things for which words stand. Definitions of words may be explicit or implicit, and may seek to report pre-existing synonymies, but they may instead be wholly or partly stipulative. Definition by abstraction seeks to define a term-forming operator by fixing the truth-conditions of identity-statements featuring terms formed by means of that operator. Such definitions are a species of implicit definition. They are typically at least partly stipulative. Definitions of things (real definitions) are typically conceived as statements about the essence of their definienda, and so not stipulative. There thus appears to be a clash between taking Hume's principle as an implicit, at least partly stipulative definition of the number operator and as a real definition of cardinal numbers. This chapter argues that this apparent tension can be resolved, and that resolving it shows how some modal knowledge can be a priori.

Dynamical Detection of Level Repulsion in the One-Particle Aubry-André Model

The analysis of level statistics provides a primary method to detect signatures of chaos in the quantum domain. However, for experiments with ion traps and cold atoms, the energy levels are not as easily accessible as the dynamics. In this work, we discuss how properties of the spectrum that are usually associated with chaos can be directly detected from the evolution of the number operator in the one-dimensional, noninteracting Aubry-André model. Both the quantity and the model are studied in experiments with cold atoms. We consider a single-particle and system sizes experimentally reachable. By varying the disorder strength within values below the critical point of the model, level statistics similar to those found in random matrix theory are obtained. Dynamically, these properties of the spectrum are manifested in the form of a dip below the equilibration point of the number operator. This feature emerges at times that are experimentally accessible. This work is a contribution to a special issue dedicated to Shmuel Fishman.

Pseudo-Hermitian position and momentum operators, Hermitian Hamiltonian, and deformed oscillators

The recently introduced by us, two- and three-parameter (p, q)- and (p, q, [Formula: see text])-deformed extensions of the Heisenberg algebra were explored under the condition of their direct link with the respective (nonstandard) deformed quantum oscillator algebras. In this paper, we explore certain Hermitian Hamiltonians build in terms of non-Hermitian position and momentum operators obeying definite [Formula: see text](N)-pseudo-hermiticity properties. A generalized nonlinear (with the coefficients depending on the particle number operator N) one-mode Bogoliubov transformation is developed as main tool for the corresponding study. Its application enables to obtain the spectrum of “almost free” (but essentially nonlinear) Hamiltonian.