We investigate squeezed states of composite bosons (cobosons) formed by pairs of spin-1/2 fermions, with emphasis on Frenkel-like cobosons. We define squeezed cobosons as eigenstates of a Bogoliubov-transformed coboson operator and derive explicit expressions for the associated quadrature variances. We show that the underlying fermionic structure leads to state-dependent modifications of the Heisenberg-Robertson uncertainty bound, which may fall below the canonical bosonic limit without implying any violation of uncertainty principles. Numerical results based on finite-dimensional matrix representations illustrate how these effects constrain the attainable squeezing. This behavior implies that experimentally accessible quantities, such as quadrature variances or noise spectra, carry information about the internal fermionic structure of the composite particles. Our framework is relevant to composite-boson systems such as tightly bound electron-hole pairs and provides a physically transparent setting to probe compositeness through observable quadrature fluctuations.

This study explores the semiclassical limit of an integrable-chaotic bosonic many-body quantum system, providing nuanced insights into its behavior. We examine classical-quantum correspondences across different interaction regimes of bosons in a triple-well potential, ranging from the integrable to the self-trapping regime, and including the chaotic one. The close resemblance between the phase-space mean projections of classical trajectories and those of Husimi distributions evokes the principle of uniform semiclassical condensation of Wigner functions of eigenstates. Notably, the resulting figures also exhibit patterns reminiscent of Jason Gallas's "shrimp" shapes.

Utilizing the Tomita–Takesaki modular theory, we derive a closed-form analytic expression for the Araki–Uhlmann relative entropy between a single-mode squeezed state and the vacuum state in a free relativistic massive scalar Quantum Field Theory within wedge regions of Minkowski spacetime. Similarly to the case of coherent states, this relative entropy is proportional to the smeared Pauli–Jordan distribution. Consequently, the Araki–Uhlmann entropy between a single-mode squeezed state and the vacuum satisfies all expected properties: it remains positive, increases with the size of the Minkowski region under consideration, and decreases as the mass parameter grows.

Ultracold atomic systems provide a versatile platform for exploring quantum phenomena, offering tunable interactions and diverse trapping geometries. In this study, we investigate a one-dimensional system of trapped fermionic atoms using the composite boson formalism, which describes pairs of opposite-spin fermions as cobosons (short for composite bosons). We solve the Schr & ouml;dinger equation for a 2 up arrow +2 down arrow fermionic system across a broad range of attractive and repulsive interactions by constructing the system's wave function as a superposition of two-coboson states. We determine key observables such as particle density profiles and two-body correlations. The density profiles calculated agree with both the Tonks-Girardeau and Lieb-Liniger limits and provide a portrait of the transition between those regimes. In the strong repulsive regime, the ansatz captures the Fridel-Wigner transition characterized by a doubling of the peaks in the density profiles. Additionally, we compute the low-lying energy spectrum and estimate the pairing gap. Our results highlight the usefulness of the coboson superposition ansatz for exploring quantum phenomena in strongly correlated few-body systems.

We numerically investigate the Araki-Uhlmann relative entropy in Quantum Field Theory, focusing on a free massive scalar field in 1+1-dimensional Minkowski spacetime. Using Tomita-Takesaki modular theory, we analyze the relative entropy between a coherent state and the vacuum state, with several types of test functions localized in the right Rindler wedge. Our results confirm that relative entropy decreases with increasing mass and grows with the size of the spacetime region, aligning with theoretical expectations.

In this work, we investigate the semiclassical limit of a simple bosonic quantum many-body system exhibiting both integrable and chaotic behavior. A classical Hamiltonian is derived using coherent states. The transition from regularity to chaos in classical dynamics is visualized through Poincar\'e sections. Classical trajectories in phase space closely resemble the projections of the Husimi functions of eigenstates with similar energy, even in chaotic cases. It is demonstrated that this correlation is more evident when projecting the eigenstates onto the Fock states. The analysis is carried out at a critical energy where the eigenstates are maximally delocalized in the Fock basis. Despite the imperfect delocalization, its influence is present in the classical and quantum properties under investigation. The study systematically establishes quantum-classical correspondence for a bosonic many-body system with more than two wells, even within the chaotic region.

A pedagogical introduction to Bell’s inequality in Quantum Mechanics is presented. Several examples, ranging from spin 1/2 to coherent and squeezed states are worked out. The generalization to Mermin’s inequalities and to GHZ states is also outlined.

We devise a general setup to investigate the violation of the Bell-CHSH inequality in the vacuum state in the context of Quantum Field Theory. We test the method with massless spinor fields in $(1+1)$-dimensional Minkowski space-time. Alice's and Bob's test functions are explicitly constructed, first by employing Haar wavelets which are then bumpified into proper test functions via a smoothening procedure relying on the Planck-taper window function. Relativistic causality is implemented by requiring the support of Alice's and Bob's test functions to be located in the left and right Rindler wedges, respectively. Violations of the Bell-CHSH inequality as close as desired to Tsirelson's bound are reported. We briefly comment on the extra portal, compared to earlier works, this opens to scrutinize Bell-CHSH inequalities with generic, interacting Quantum Field Theories.

A relativistic Quantum Field Theory framework is devised for Mermin's inequalities. By employing smeared Dirac spinor fields, we are able to introduce unitary operators which create, out of the Minkowski vacuum |0〉, GHZ-type states. In this way, we are able to obtain a relation between the expectation value of Mermin's operators in the vacuum and in the GHZ-type states. We show that Mermin's inequalities turn out to be maximally violated when evaluated on these states.

The violation of Mermin's inequalities is analyzed by making use of two different Bell setups built with pseudospin operators. Employing entangled states defined by means of squeezed and coherent states, the expectation value of Mermin's polynomials Mn is evaluated for n = 3 and n = 4. In each case, we analyze the correlator ⟨Mn⟩ and identify the set of parameters leading to the violation of Mermin's inequalities and to the saturation of the bound predicted by Quantum Mechanics.

In this work, using a Noisy Intermediate-Scale Quantum (NISQ) framework, we obtain the gap of a Bardeen–Cooper–Schrieffer (BCS) Hamiltonian. This could lead to interesting implications for superconductivity research. For such task, we choose to use the Variational Quantum Deflation and analyze the hardware restrictions that are needed to find the energy spectra on current quantum hardware.We also compare two different kinds of classical optimizers, Constrained Optimization BY Linear Approximations (COBYLA) and Simultaneous Perturbation Stochastic Approximation (SPSA), and study the effect of decoherence caused by the presence of noise when using simulations in real devices. We apply our method for an example with both 2 and 5 qubits. Furthermore, we show how to approximate the gap within one standard deviation, even with the presence of noise.

Quantum computing, along with quantum metrology and quantum communication, are disruptive technologies that promise, in the near future, to impact different sectors of academic research and industry. Among the computational challenges with great interest in science and industry are the inversion problems. These kinds of numerical procedures can be described as the process of determining the cause of an event from measurements of its effects. In this paper, we apply a recursive quantum algorithm to a D-Wave quantum annealer to solve a small scale seismic inversions problem. We compare the obtained results from the quantum computer to those derived from a classical algorithm. The accuracy achieved by the quantum computer is at least as good as that of the classical computer.

We put forth a quantum simulation of a stroboscopic two-stroke thermal engine in the IBMQ processor. The system consists of a quantum spin chain connected to two baths at their boundaries, prepared at different temperatures using the variational quantum thermalizer algorithm. The dynamics alternates between heat and work strokes, which can be separately designed using independent quantum circuits. The results show good agreement with theoretical predictions, showcasing IBMQ as a powerful tool to study thermodynamics in the quantum regime, as well as the implementation of variational quantum algorithms in real-world quantum computers. It also opens the possibility of simulating quantum heat transport across a broad range of chain geometries and interactions.

We focus on using an architecture similar to the beta-Variational Autoencoder (beta-VAE) to discriminate if a quantum state is entangled or separable based on measurements. We split the data into two sets, the set of local and correlated measurements. Using the latent space, which is a low dimensional representation of the data, we show that restricting ourselves to the set of local data it is not possible to distinguish between entangled and separable states. Meanwhile, when considering both correlated and local measurements, an accuracy of over 80% is attained in the structure of the latent space. (C) 2021 The Authors. Published by Elsevier B.V.

Multiparticle entangled states, essential ingredients for modern quantum technologies, are routinely generated in experiments of atomic Bose-Einstein condensates (BECs). However, the entanglement in ultracold interacting Fermi gases has not been yet exploited. In this work, by using an ansatz of composite bosons, we show that many-particle entanglement between two fermionic ensembles localized in spatially separated modes can be generated by splitting an ultracold interacting Fermi gas in the (molecular) BEC regime. This entanglement relies on the fundamental fermion exchange symmetry of molecular constituents and might be used for implementing Bell test of quantum nonlocality in oncoming experiments.

Feshbach molecules forming a Bose–Einstein condensate (BEC) behave as non-ideal bosonic particles due to their underlying fermionic structure. We study the observable consequences of the fermion exchange interactions in the interference of molecular BECs for entangled-enhanced precision measurements. Our many-body treatment of the molecular condensate is based on an ansatz of composite two-fermion bosons which accounts for all possible fermion exchange correlations present in the system. The Pauli principle acts prohibitively on the particle fluctuations during the interference process leading to a loss of precision in phase estimations. However, we find that, in the regime where molecular dissociations do not jeopardize the interference dynamics, measurements of the phase can still be performed with a precision beyond the classical limit comparable to atomic interferometers. We also show that the effects of Pauli principle increases with the noise of the particle detectors such that molecular interferometers would require more efficient detectors.

We show that an ansatz based on independent composite bosons [Phys. Rep. 463, 215 (2008)] accurately describes the condensate fraction of molecular Bose-Einstein condensates in ultracold Fermi gases. The entanglement between the fermionic constituents of a single Feshbach molecule then governs the many-particle statistics of the condensate, from the limit of strong interaction to close to unitarity. This result strengthens the role of entanglement as the indispensable driver of composite-boson behavior. The condensate fraction of fermion pairs at zero temperature that we compute matches excellently previous results obtained by means of fixed-node diffusion Monte Carlo methods and the Bogoliubov depletion approximation. This paves the way towards the exploration of the BEC-BCS crossover physics in mixtures of cold Fermi gases with an arbitrary number of fermion pairs as well as the implementation of Hong-Ou-Mandel-like interference experiments proposed within coboson theory.

Memoryless time evolutions are ubiquitous in nature but often correspond to a resolution-induced approximation, i.e. there are correlations in time whose effects are undetectable. Recent advances in the dynamical control of small quantum systems provide the ideal scenario to probe some of these effects. Here we experimentally demonstrate the precise induction of memory effects on the evolution of a quantum coin (qubit) by correlations engineered in its environment. In particular, we design a collisional model in Nuclear Magnetic Resonance (NMR) and precisely control the strength of the effects by changing the degree of correlation in the environment and its time of interaction with the qubit. We also show how these effects can be hidden by the limited resolution of the measurements performed on the qubit. The experiment reinforces NMR as a test bed for the study of open quantum systems and the simulation of their classical counterparts.

We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the gl(2)-invariant R-matrix for the two-site Bose–Hubbard model. Using a binomial expansion of the n-th power of a sum of two operators we get and solve a recursion equation. We calculate the scalar product and the norm of the Bethe vectors states. The form factors of the imbalance current operator are also computed.

We investigate by means of a variational approach the effective potential of a 5D U(1) scalar model at finite temperature and compactified on S1 and S1/Z2 as well as the corresponding 4D model obtained through a trivial dimensional reduction. We are particularly interested in the behavior of the thermal masses of the scalar field with respect to the Wilson line phase and the results obtained are compared with those coming from a one-loop effective potential calculation. We also explore the nature of the phase transition.