相关论文: Holstein-Primakoff/Bogoliubov Transformations and …
This article presents a squeezing transformation for quantum systems associated to finite vector spaces. The physical idea of squeezing here is taken from the action of the usual squeezing operator over wave functions defined on a real…
Stabilizer states, which are also known as the Clifford states, have been commonly utilized in quantum information, quantum error correction, and quantum circuit simulation due to their simple mathematical structure. In this work, we apply…
We theoretically analyze the ground state of weakly interacting bosons in the flux ladder -- the system that has been recently realized by means of ultacold atoms in the specially designed optical lattice [M. Atala, et al., Nat. Phys. 10,…
Recent studies on non-perturbation aspects of noncommutative quantum mechanics explored a new type of boson commutation relations at the deformed level, described by deformed annihilation-creation operators in noncommutative space. This…
The transformer architecture, known for capturing long-range dependencies and intricate patterns, has extended beyond natural language processing. Recently, it has attracted significant attention in quantum information and condensed matter…
This paper explores the Bogoliubov transformation's extension to two-mode squeezed states, building on our previous work with Virasoro-squeezing. We establish the Virasoro-Bogoliubov transformation as a non-linear extension of the…
By extending the usual two-mode squeezing operator $S_{2}=\exp [ i\lambda (Q_{1}P_{2}+Q_{2}P_{1}) ] $ to the three-mode squeezing operator $S_{3}=\exp {i\lambda [ Q_{1}(P_{2}+P_{3}) +Q_{2}(P_{1}+P_{3}) +Q_{3}(P_{1}+P_{2}) ]} $, we obtain…
The Bogoliubov approximation is used to study the excited states of a dilute gas of $N$ atomic bosons trapped in an isotropic harmonic potential characterized by a frequency $\omega_0$ and an oscillator length $d_0 =…
Recent experimental breakthroughs in the treatment of dilute Bose gases have renewed interest in their quantum mechanical description, respectively in approximations to it. The ground state properties of dilute Bose gases confined in…
Consider two free Hamiltonians for the same scalar field with two different masses. Wefind a squeeze operator which maps the ground state of one to the other. The operatoris described in both the Dirac and also the Schrodinger…
We develop a scheme to prepare a desired state or subspace in high-dimensional Hilbert-spaces using repeated applications of a single static projection operator onto the desired target and fixed unitary dynamics. Benchmarks against other…
We consider a model of coupled oscillators which can be seen as a gain and loss system. In the attempt to quantize the system we propose a new definition of multiplication between distributions, and we check that this definition can be…
A "squeezed-vacuum" state considered in quantum optics is shown to be realized in the ground-state wavefunction for the bilayer quantum Hall system at the total Landau level filling of $\nu=1/m$ (m: odd integer). This is derived in the…
We develop a new method of representation of quantum states in terms of the displaced number states. We call it representation, where is an amplitude of the base displaced states. In particular, representation was obtained for set of the…
We consider the transformation of Hamilton operators under various sets of quantum operations acting simultaneously on all adjacent pairs of particles. We find mappings between Hamilton operators analogous to duality transformations as well…
We study the classification problem of mixed states in two-dimensional quantum spin systems in the operator algebraic framework of quantum statistical mechanics. We associate a braided $C^*$-tensor category to each state satisfying a…
Fragmented Bose-Einstein condensates are large systems of identical bosons displaying \emph{multiple} macroscopic occupations of one-body states, in a suitable sense. The quest for an effective dynamics of the fragmented condensate at the…
Stators, which may be intuitively defined as "half states, half operators" are mathematical objects which act on two Hilbert spaces and utilize entanglement to create remote operations and exchange information between two physical systems.…
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated…
In this paper we consider squares of pseudo-bosonic ladder operators and we use them to produce explicit examples of eigenstates of certain operators satisfying a deformed $\mathfrak{su}(1,1)$ Lie algebra. We show how these eigenstates may,…