Vacuum State Research Articles

Gain sensitivity of the Mach–Zehnder interferometer by photon subtraction

Abstract The phase sensitivity of a Mach–Zehnder (MZ) interferometer with a two-mode squeezed vacuum (TMSV) probe state is studied. At the initial stage, the TMSV state is deterministically converted into two single-mode squeezed vacuum (SMSV) states, from each of which photons are subtracted via photon-number resolving measurement in auxiliary measurement modes. The new probe state can already demonstrate gain sensitivity of more than 20 dB with input squeezing of 5 dB and follow Heisenberg scaling. The phase sensitivity of the MZ interferometer, estimated by measuring the intensity difference of two measurement-induced continuous variable states, can surpass the ultimate one with SMSV probe states, at least, with squeezing less than 5 dB. In general, the strategy with preliminary subtraction of photons significantly increases the estimate potential of weakly squeezed states as the probe in MZ phase-dependent interferometry; in particular, it is more effective compared to generating highly squeezed TMSV states or SMSV states.

Bubble velocities and oscillon precursors in first-order phase transitions

Abstract Metastable ‘false’ vacuum states are an important feature of the Standard Model of particle physics and many theories beyond it. Describing the dynamics of a phase transition out of a false vacuum via the nucleation of bubbles is essential for understanding the cosmology of vacuum decay and the full spectrum of observables. In this paper, we study vacuum decay by numerically evolving ensembles of field theories in 1+1 dimensions from a metastable state. We demonstrate that for an initial Bose-Einstein distribution of fluctuations, bubbles form with a Gaussian spread of center-of-mass velocities and that bubble nucleation events are preceded by an oscillon — a long-lived, time-dependent, pseudo-stable configuration of the field. Defining an effective temperature from the long-wavelength amplitude of fluctuations in the ensemble of simulations, we find good agreement between theoretical finite temperature predictions and empirical measurements of the decay rate, velocity distribution and critical bubble solution. We comment on the generalization of our results and the implications for cosmological observables.

Some Fock spaces with depth two action

Abstract The subject of this article is operators represented on a Fock space which act only on the two leading components of the tensor. We unify the constructions from [Ans07, BL09, BL11, LS08] and extend a number of results from these articles to our more general setting. The results include the quadratic relation satisfied by the kernel of the free cumulant generating function, the resolvent form of the generating function for the Wick polynomials, and classification results for the case when the vacuum state on the operator algebra is tracial. We handle the generating functions in infinitely many variables by considering their matrix-valued versions.

Implementation of time-dependent Hartree–Fock in real space

Abstract Time-dependent Hartree–Fock (TDHF) is one of the fundamental post-Hartree–Fock (HF) methods to describe excited states. In its Tamm-Dancoff form, equivalent to Configuration Interaction Singles, it is still widely used and particularly applicable to big molecules where more accurate methods may be unfeasibly expensive. However, it is rarely implemented in real space, mostly because of the expensive nature of the exact-exchange potential in real space. Compared to widely used Gaussian-type orbitals (GTO) basis sets, real space often offers easier implementation of equations and more systematic convergence of Rydberg states, as well as favorable scaling, effective domain parallelization, flexible boundary conditions, and ability to treat model systems. We implemented TDHF in the Octopus real-space code as a step toward linear-response hybrid time-dependent density-functional theory (TDDFT), other post-HF methods, and ensemble density-functional theory methods involving exact exchange. Calculation of HF’s non-local exact exchange is very expensive in real space. We overcome this limitation with Octopus’ implementation of Adaptively Compressed Exchange, and find the appropriate mixing scheme and starting point to complete the ground-state calculation in a practical amount of time, and thus enable TDHF. We compared our results to those from GTOs on a set of small molecules and confirmed close agreement of results, though with larger deviations than in the case of semi-local TDDFT. We find that convergence of TDHF demands a finer real-space grid than semi-local TDDFT. We also present the subtleties in benchmarking a real-space calculation against GTOs, relating to Rydberg and vacuum states.

Detecting quantum vacuum fluctuations of the electromagnetic field

Abstract Quantum vacuum fluctuations of the electromagnetic field result in two signatures on a harmonically trapped charged particle: a shift from the natural trap frequency and generation of quantum coherences. We assess the role of the long-wavelength and rotating-wave approximations in estimating this frequency shift. We estimate the magnitude of the frequency shift using parameters from a single-electron cyclotron experiment and also demonstrate how the dependence of the frequency shift on the magnetic field of the cyclotron is tied to the rotating-wave approximation. We expect the frequency shift to be observable in future experiments. We also suggest a possible route to detecting vacuum-generated quantum coherences. These experiments should settle the debate on
the choice of approximations and gauge in capturing the effect of the quantum vacuum fluctuations.

Choice of vacuum state and the relation between inflationary and Planck scales

Choice of vacuum state and the relation between inflationary and Planck scales

Glauber-Sudarshan states, wave functional of the Universe and the Wheeler-De Witt equation

One of the pertinent question in the analysis of de Sitter as an excited state is what happens to the Glauber-Sudarshan states that are off-shell, i.e. the states that do not satisfy the Schwinger-Dyson equations. We argue that these Glauber-Sudarshan states, including the on-shell ones, are controlled by a bigger envelope wave functional namely a wave functional of the universe which surprisingly satisfies a Wheeler-De Witt equation. We provide various justification of the aforementioned identification including the determination of the emergent Hamiltonian constraint appearing in the Wheeler-De Witt equation that is satisfied by both the on- and off-shell states. Our analysis provides further evidence of why a transient four-dimensional de Sitter phase in string theory should be viewed as an excited state over a supersymmetric warped Minkowski background and not as a vacuum state.

Yukawa theory in non-perturbative regimes: towards confinement, exact β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-function and conformal phase

We study possible hints towards confinement in a Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Z}_2$$\\end{document}-invariant Yukawa system with massless fermions and a real scalar field in the strongly-coupled regime. Using the tools developed for studying non-perturbative physics via Jacobi elliptical functions, for a given but not unique choice of the vacuum state, we find the exact Green’s function for the scalar sector so that, after integrating out the scalar degrees of freedom, we are able to recover the low-energy limit of the theory that is a fully non-local Nambu–Jona–Lasinio (NJL) model. We provide an analytical result for the renormalization group (RG) running of the self-interaction coupling in the scalar sector in the strongly-coupled regime. In the fermion sector, we provide some clues towards confinement, after deriving the gap equation with the non-local NJL model, a property which is well-known to not emerge in the local limit of this model. We conclude that, for the scalar-Yukawa theory in the non-perturbative domain with our choice of the vacuum state, the fundamental fermions of the theory form bound states and cannot be observed as asymptotic states.

What is Light, Really? A Quantum Dialectical View

Radiant energy in the form of visible light has been and still remains the most mysterious and venerated object in human history. Gradual understanding of the nature of light now in its very wide range of energy, both above and below the visible range; has led to the proliferation of technologies, especially after the recognition of its quantum nature. Although impressive knowledge about the nature of light, its properties, its source, and its interaction with other existing matter, etc., have been gained and profitably utilized in technologies; its fundamental unit as a discrete point particle or an extended continuous wavelet, as well as its mass, still remains a subject of intense debate among the physicists. Understanding the enigmatic properties and the nature of light as difficult as it proved to be; understanding the velocity of its propagation proved to be the most misunderstood aspect of light. As has been shown through some recent publications by this author, the false axiomatic notion of Albert Einstein at the turn of the 20th century, about the universal and absolute constancy (in vacuum) of the velocity c of light; caused the century-long confusion, paradoxes, myths and ironically, the darkest period of modern physics and cosmology! Another wrong centuries-old axiomatic notion of Isaac Newton about the one-sided universal gravitational attraction of matter, acted in a synergistic way with Einstein’s false axiomatic notion about light; to create the modern and sophisticated ruling mythology of the “Big Bang” creation of the universe, undermining scientific progress both in theoretical physics and in cosmology, since Copernicus and Johannes Kepler. It can now be demonstrated that this new mythology has absolutely no basis in objective reality and is the product of brain-cooked and abstract mathematical fabrications based on an axiomatic truth and apparently willful deceptions by official science. A quantum dialectical approach reveals that light is composed of point particles (photons) with a wide range of energy, velocity, and mass; over the whole electromagnetic spectrum, from the microwave to the highest energy gamma-ray photons. The only difference from other matter particles is that photons exist only in their free elementary state and are created instantly (until absorbed) from their virtual existence in matter atoms or in the quantum vacuum; in this infinite, eternal, and ever-changing universe; thereby resolving all mysteries about light.

Generation of squeezed vacuum state in the millihertz frequency band

The detection of gravitational waves has ushered in a new era of observing the universe. Quantum resource advantages offer significant enhancements to the sensitivity of gravitational wave observatories. While squeezed states for ground-based gravitational wave detection have received marked attention, the generation of squeezed states suitable for mid-to-low-frequency detection has remained unexplored. To address the gap in squeezed state optical fields at ultra-low frequencies, we report on the first direct observation of a squeezed vacuum field until Fourier frequency of 4 millihertz with the quantum noise reduction of up to 8.0 dB, by the employment of a multiple noise suppression scheme. Our work provides quantum resources for future gravitational wave observatories, facilitating the development of quantum precision measurement.

Frequency tuning of a squeezed vacuum state using interferometric enhanced acousto-optic effect

Quantum frequency conversion is one of the important tools for quantum information processing. So far, the frequency conversion of continuous variable quantum state in radio frequency range has not been demonstrated yet. Here, we experimentally demonstrate the optical frequency fine tuning of a squeezed vacuum state by using an acousto-optic modulator based bi-frequency interferometer. The systematic efficiency of the frequency tuning device is 91%, which is only confined by the optical transmission efficiency of the acousto-optic modulators. The amount of frequency tuning is 80 MHz, which is orders of magnitude larger than the line-width of the laser used to generate the squeezed state and can, in principle, be further extended. A squeezed vacuum state with −3.47 ± 0.02 dB squeezing level is sent to the frequency tuning device, and a squeezing level of −1.98 ± 0.02 dB is directly measured by a fiber coupled homodyne detector after the frequency tuning. Our scheme can also be applied to a variety of other quantum optical states as well and will serve as a handy tool for quantum networks.

Energy change and Landauer’s principle in the interaction between qubit and quantum field theory

We give a general description of the system evolution under the interaction between qubit and quantum field theory up to the second order perturbation, which is also referred to as the simplified model of light-matter interaction. The results are classified into rotating and counter-rotating wave terms, the former corresponding to stimulated absorption and emission, and the latter to Unruh and anti-Unruh effects. We obtain not only the reduced density matrix of the qubit, but also the backreaction obtained by quantum field theory as the environment. The result shows that the energy variation of the quantum field theory is related to trajectory and the initial state of the qubit, the expectation values of the linear and quadratic field operators, and the temporal order product operator. When the qubit is in accelerated motion, the conventional Unruh effect causes the vacuum state to possess a “temperature”, which raises some doubts about the validity of Landauer’s principle. We prove that Landauer’s principle still holds for any state of motion.

Effect of noisy environment on secure quantum teleportation of unimodal Gaussian states

Quantum networks rely on quantum teleportation, a process where an unknown quantum state is transmitted between sender and receiver via entangled states and classical communication. In our study, we utilize a continuous variable two-mode squeezed vacuum state as the primary resource for quantum teleportation, shared by Alice and Bob, while exposed to a squeezed thermal environment. Secure quantum teleportation necessitates a teleportation fidelity exceeding 2/3 and the establishment of two-way steering of the resource state. We investigate the temporal evolution of steering and teleportation fidelity to determine critical parameter values for secure quantum teleportation of a coherent Gaussian state. Our findings reveal constraints imposed by temperature, dissipation rate, and squeezing parameters of the squeezed thermal reservoir on the duration of secure quantum teleportation. Intriguingly, we demonstrate that increasing the squeezing parameter of the initial state effectively extends the temporal window for a successful secure quantum teleportation.

Numerical optimization of quantum vacuum signals

The identification of prospective scenarios for observing quantum vacuum signals in high-intensity laser experiments requires both accurate theoretical predictions and the exploration of high-dimensional parameter spaces. Numerical simulations address the first requirement, while optimization provides an efficient solution for the second one. In the present work, we put forward Bayesian optimization as a new and powerful means to optimize photonic quantum vacuum signals. We demonstrate its great potential on the example of the well-studied case of two-beam collisions. Apart from providing an ideal benchmark case, this immediately gives new physics results. Namely, Bayesian optimization allows us to find the optimal waist sizes for beams with elliptic cross sections, and to identify the specific physical process leading to a discernible signal in a coherent harmonic focusing configuration scenario. Published by the American Physical Society 2024

Monte Carlo methods in the manifold of Hartree-Fock-Bogoliubov wave functions.

We explore the possibility of implementing random walks in the manifold of Hartree-Fock-Bogoliubov wave functions. The goal is to extend state-of-the-art quantum Monte Carlo approaches, in particular the constrained-path auxiliary-field quantum Monte Carlo technique, to systems where finite pairing order parameters or complex pairing mechanisms, e.g., Fulde-Ferrell-Larkin-Ovchinnikov pairing or triplet pairing, may be expected. Leveraging the flexibility to define a vacuum state tailored to the physical problem, we discuss a method to use imaginary-time evolution of Hartree-Fock-Bogoliubov states to compute ground state correlations, extending beyond situations spanned by current formalisms. Illustrative examples are provided.

Entanglement, quantum steering, and Bell nonlocality in the Tavis–Cummings system

In this work, we focus on quantum correlations, specifically entanglement, quantum steering, and Bell nonlocality within the Tavis–Cummings model. This study investigates these quantum correlations in the context of various fields existing in the cavity. The findings reveal the hierarchy of quantum correlations—entanglement, quantum steering, and Bell nonlocality—in two two-level atoms under the influence of thermal, coherent, and squeezed vacuum states. The dynamic process demonstrates certain oscillations, with particular emphasis on the presence of asymmetric quantum steering.

Cosmological particle creation using an equal-time Wigner formalism

It is well known that the expansion of the universe can create particles. However, due to ambiguities when defining particles during the expansion, there are still debates about how to choose vacuum and particle states. To clarify how particles are produced in an expanding universe, we study the creation of real scalar particles in flat Friedmann-Lemaître-Robertson-Walker spacetimes by using a recently developed equal-time Wigner formalism. By comparing this quantum kinetic formalism with the standard Bogoliubov approach, we make a natural definition of a particle number in terms of kinetic phase-space functions, which we then compare with common adiabatic particle numbers. With inspiration from flat spacetime QED, we perform numerical calculations and discuss the interpretation of the particle numbers in terms of a hypothetical switch-off in the expansion rate. Finally, we consider how this interpretation is affected by regularization. Published by the American Physical Society 2024

Analogical atomic effects of graphene nanostructure induced by nonlinearity.

A scheme to construct analogical atoms using graphene nanostructures via quantum nonlinearity is proposed. Due to the strong field localization capability of graphene plasmons and the significant intrinsic nonlinearity of graphene, a strong nonlinear optical response can be realized even with single-photon excitation. In this process, the quantum vacuum localized plasmonic mode plays a crucial role in achieving the third-order multi-photon nonlinear effect. The eigenfrequency of the nanostructure can shift by an amount tens of times larger than the decay rate, causing the nanostructure cavity to exhibit atomic-like behaviors. Furthermore, multilevel atoms can be constructed through the interaction of composite graphene nanostructures. The parameters of these atoms can be manipulated by adjusting the nanostructure size, Fermi energy, and other parameters. This research holds significant potential for applications in highly integrated, controllable nanophotonics.

Concentration and cavitation in the Riemann solutions to the Umami Chaplygin Euler equations

The concentration phenomena in fluid dynamics can be mathematically described by delta-shocks. With the introduction of flux-function, the Riemann problem for the Euler system with Umami Chaplygin gas equation of state is discussed. What Umami Chaplygin gas means is that the fluid obeys the pressure–density relation where the pressure is negative and is a new generalization of Chaplygin gas. The solutions with six kinds of structures are constructed. Unlike the Chaplygin gas, the delta-shock occurs in solutions, even though the system is strictly hyperbolic and two characteristic fields are genuinely nonlinear. The generalized Rankine–Hugoniot relation and entropy condition for delta-shock are clarified. Additionally, the phenomena of concentration and cavitation and the formation of delta-shocks and vacuum states in solutions are identified and analyzed as the Umami Chaplygin gas pressure and flux-function vanish simultaneously. It is proved that as the pressure and flux-function drop to zero, any solution consisting of two shocks tends to the delta-shock solution of the pressureless Euler system, and any solution consisting of two rarefaction waves tends to the vacuum Riemann solution of the pressureless Euler system. Finally, some numerical results exhibiting the processes of formation of delta-shocks and vacuum states are presented.

Vacuum entanglement probes for ultra-cold atom systems

Abstract This study explores the transfer of nonclassical correlations from an ultra-cold atom system to a pair of pulsed laser beams. Through nondestructive local probe measurements, we introduce an alternative to destructive techniques for mapping Bose–Einstein Condensate (BEC) entanglement. Operating at ultra-low temperatures, BEC density fluctuations emulate a relativistic vacuum field. We show that lasers can serve as Unruh–DeWitt detectors for vacuum BEC phonons. A quantum vacuum holds intrinsic entanglement, transferable to distant probes briefly interacting with it—a phenomenon termed ‘entanglement harvesting’. Our study accomplishes two primary objectives: first, establishing a mathematical connection between a pair of pulsed laser probes interacting with an effective relativistic field and the entanglement harvesting protocol; and second, to closely examine the potential and persisting obstacles for realising this protocol in an ultra-cold atom experiment.