We study the structure of vacuum entanglement for two complimentary segments of a linear harmonic chain, applying the modewise decomposition of entangled gaussian states discussed in \cite {modewise}. We find that the resulting entangled mode shape hierarchy shows a distinctive layered structure with well defined relations between the depth of the modes, their characteristic wavelength, and their entanglement contribution. We re-derive in the strong coupling (diverging correlation length) regime, the logarithmic dependence of entanglement on the segment size predicted by conformal field theory for the boson universality class, and discuss its relation with the mode structure. We conjecture that the persistence of vacuum entanglement between arbitrarily separated finite size regions is connected with the localization of the highest frequency innermost modes.
Description of detection and emission in terms of the photon localization is discussed. It is shown that the standard representation of plane waves of photons should be revised to take into consideration the boundary conditions caused by the presence of quantum emitters and detectors. In turn, the change of the boundary conditions causes spatially inhomogeneous structure of the electromagnetic vacuum which leads to the increase of the vacuum noise over the level predicted in the frame of the model of plane photons.
By using the invariant method we find one-parameter squeezed Gaussian states for both time-independent and time-dependent oscillators. The squeezing parameter is expressed in terms of energy expectation value for time-independent case and represents the degree of mixing positive and negative frequency solutions for time-dependent case. A {\it minimum uncertainty proposal} is advanced to select uniquely vacuum states at each moment of time. We show that the Gaussian states with minimum uncertainty coincide with the true vacuum state for time-independent oscillator and the Bunch-Davies vacuum fo…
The system of oscillator interacting with vacuum is considered as a problem of random motion of quantum reactive harmonic oscillator (QRHO). It is formulated in terms of a wave functional regarded as complex probability process in the extended space. This wave functional obeys some stochastic differential equation (SDE). Based on the nonlinear Langevin type SDE of second order, introduced in the functional space R{W(t)}, the variables in original equation are separated. The general measure in the space R{W(t)} of the Fokker-Plank type is obtained and expression for total wave function (wave mi…
We investigate a simple arrangement of coupled harmonic oscillators which brings out some interesting effects concerning creation of entanglement. It is well known that if each member in a linear chain of coupled harmonic oscillators is prepared in a ``classical state'', such as a pure coherent state or a mixed thermal state, no entanglement is created in the rotating wave approximation. On the other hand, if one of the oscillators is prepared in a nonclassical state (pure squeezed state, for instance), entanglement may be created between members of the chain. In the setup considered here, we …
In this paper, we present a rigorous analysis of symmetry and underlying physics of the nonlinear two-mode system driven by a harmonic mixing field, by means of multiple scale asymptotic analysis method. The effective description in the framework of the second-order perturbative theory provides an accurate picture for understanding the Floquet eigenspectrum and dynamical features of the nonlinear two-mode system, showing full agreement with the prediction of symmetry considerations. We find that two types of symmetries play significant role in the dynamical features of this model, the mechanis…
Disordered geometrical boundaries such as rough surfaces induce important modifications to the mode spectrum of the electromagnetic quantum vacuum. In analogy to Anderson localization of waves induced by a random potential, here we show that the Casimir-Polder interaction between a cold atomic sample and a rough surface also produces localization phenomena. These effects, that represent a macroscopic manifestation of disorder in quantum vacuum, should be observable with Bose-Einstein condensates expanding in proximity of rough surfaces.
We propose a photonics-based, continuous-variable (CV) form of remote entanglement utilizing strictly second-order nonlinear optical interactions that does not require the implementation of a state-projective measurement (i.e. remote entanglement without conditioning). This scheme makes use of two separate down-converters, wherein the corresponding nonlinear crystals are driven by strong classical fields as prescribed by the parametric approximation, as well as a fully quantum mechanical model of nondegenerate second harmonic generation (SHG) whose evolution is described by the trilinear Hamil…
Squeezed states of harmonic oscillators are a central resource for continuous-variable quantum sensing, computation and communication. Here we propose a method for the generation of very good approximations to highly squeezed vacuum states with low excess anti-squeezing using only a few oscillator-qubit coupling gates through a Rabi-type interaction Hamiltonian. This interaction can be implemented with several different methods, which has previously been demonstrated in superconducting circuit and trapped-ion platforms. The protocol is compatible with other protocols manipulating quantum harmo…
We show that coherent harmonic focusing provides an efficient mechanism to boost all-optical signatures of quantum vacuum nonlinearity in the collision of high-intensity laser fields, thereby offering a promising route to their first experimental detection. Assuming two laser pulses of given parameters at our disposal, we demonstrate a substantial increase of the number of signal photons measurable in experiments where one of the pulses undergoes coherent harmonic focusing before it collides with the fundamental-frequency pulse. Imposing a quantitative criterion to discern the signal photons f…
We apply the Floquet-Green operator formalism to the case of a harmonically-driven two-level system. We derive exact expressions for the quasi-energies and the components of the Floquet eigenstates with the use of continued fractions. We study the avoided crossings structure of the quasi-energies as a function of the strength of the driving field and give an interpretation in terms of resonant multi-photon processes. From the Floquet eigenstates we obtain the time-evolution operator. Using this operator we study Dynamic Localization and High-order Harmonic Generation in the non-perturbative re…
The time evolution of driven two-level systems in the far off-resonance regime is studied analytically. We obtain a general first-order perturbative expression for the time-dependent density operator which is applicable regardless of the coupling strength value. In the strong field regime, our perturbative expansion remains valid even when the far off-resonance condition is not fulfilled. We find that, in the absence of dissipation, driven two-level systems exhibit coherent population trapping in a certain region of parameter space, a property which, in the particular case of a symmetric doubl…
We show that the presence of a harmonic trap may in itself lead to many-body localization for cold atoms confined in that trap in a quasi-one-dimensional geometry. Specifically, the coexistence of delocalized phase in the center of the trap with localized region closer to the edges is predicted with the borderline dependent on the curvature of the trap. The phenomenon, similar in its origin to Stark localization, should be directly observed with cold atomic species. We discuss both the spinless and the spinful fermions, for the latter we address Stark localization at the same time as it has no…
Generation of bright quantum high-order harmonic driven by combined coherent and bright squeezed vacuum light
Institute of Atomic and Molecular Physics, Jilin University（吉林大学原子与分子物理研究所）；Jilin Provincial Key Laboratory of Transient Quantum Process Control and Application, Jilin University（吉林大学瞬态量子过程控制与应用吉林省重点实验室）；College of Physics, Jilin University（吉林大学物理学院）
Decoherence remains one of the most serious challenges to the implementation of quantum technology. It appears as a result of the transformation over time of a quantum superposition state into a classical mixture due to the quantum system interacting with the environment. Since quantum systems are never completely isolated from their environment, decoherence therefore cannot be avoided in realistic situations. Decoherence has been extensively studied, mostly theoretically, because it has many important implications in quantum technology, such as in the fields of quantum information processing,…
Extension of the formalism of Q.M. to resolve mathematical anomalies in the structure of anti-unitary operators; implications for vacuum structure and spin-statistics arising from an analysis applied to the S.H.O. Outline of the derived properties of the S.M. Higgs boson.
We consider the thermodynamic properties of the squeezed vacuum state of a frequency--modulated quantum harmonic oscillator. We analytically relate the squeezing parameter to the irreversible work and the degree of nonadiabaticity of the frequency transformation. We furthermore determine the optimal modulation that leads to maximal squeezing, and discuss its implementation as well as the detection of squeezing in single cold ion traps.
We examine the entanglement induced by an angular momentum coupling between two harmonic systems. The Hamiltonian corresponds to that of a charged particle in a uniform magnetic field in an anisotropic quadratic potential, or equivalently, to that of a particle in a rotating quadratic potential. We analyze both the vacuum and thermal entanglement, obtaining analytic expressions for the entanglement entropy and negativity through the gaussian state formalism. It is shown that vacuum entanglement diverges at the edges of the dynamically stable sectors, increasing with the angular momentum and sa…
We review a number of ideas related to area law scaling of the geometric entropy from the point of view of condensed matter, quantum field theory and quantum information. An explicit computation in arbitrary dimensions of the geometric entropy of the ground state of a discretized scalar free field theory shows the expected area law result. In this case, area law scaling is a manifestation of a deeper reordering of the vacuum produced by majorization relations. Furthermore, the explicit control on all the eigenvalues of the reduced density matrix allows for a verification of entropy loss along …
High-order correlations and ultrafast Wigner negativities in bright-squeezed-vacuum-driven high-harmonic generation
Max Planck Institute for the Structure and Dynamics of Matter（马普固体与结构研究所）；Guangdong Technion-Israel Institute of Technology（广东以色列理工学院）；Technion–Israel Institute of Technology（以色列理工学院）；Initiative for Computational Catalysis (ICC), Flatiron Institute（Flatiron研究所计算催化倡议）
Emission of high-order harmonics from solids provides a new avenue in attosecond science. On one hand, it allows to investigate fundamental processes of the non-linear response of electrons driven by a strong laser pulse in a periodic crystal lattice. On the other hand, it opens new paths toward efficient attosecond pulse generation, novel imaging of electronic wave functions, and enhancement of high-order harmonic generation (HHG) intensity. A key feature of HHG in a solid (as compared to the well-understood phenomena of HHG in an atomic gas) is the delocalization of the process, whereby an e…
Modular theory of operator algebras and the associated KMS property are used to obtain a unified description for the thermal aspects of the standard heat bath situation and those caused by quantum vacuum fluctuations from localization. An algebraic variant of lightfront holography reveals that the vacuum polarization on wedge horizons is compressed into the lightray direction. Their absence in the transverse direction is the prerequisite to an area (generalized Bekenstein-) behavior of entropy-like measures which reveal the loss of purity of the vacuum due to restrictions to wedges and their h…
A system of two independent Bosonic Harmonic Oscillators is converted into the respective fourth-order derivative Pais-Uhlenbeck oscillator model. The conversion procedure displays transparently how the quantization of the fourth-order derivative Pais-Uhlenbeck oscillator has to be performed in order not to suffer from the divergence problems of the vacuum state and path integrals as conjectured most recently by P. D. Mannheim in his article ``Determining the normalization of the quantum field theory vacuum, with implications for quantum gravity" [arXiv:2301.13029 [hep-th]]. In order to make t…
The phenomenon of Many-Body Stark Localization of bosons in tilted optical lattice is studied. Despite the fact that no disorder is necessary for Stark localization to occur, it is very similar to well known many body localization (MBL) in sufficiently strong disorder. Not only the mean gap ratio reaches poissonian value as characteristic for localized situations but also the eigenstates reveal multifractal character as in standard MBL. Stark localization enables a coexistence of spacially separated thermal and localized phases in the harmonic trap similarly to fermions. Stark localization may…
Quantum harmonic analysis on phase space is shown to be linked with localization operators. The convolution between operators and the convolution between a function and an operator provide a conceptual framework for the theory of localization operators which is complemented by an appropriate Fourier transform, the Fourier-Wigner transform. We use Lieb's uncertainty principle to establish a sharp Hausdorff-Young inequality for the Fourier-Wigner transform. Noncommutative Tauberian theorems due to Werner allow us to extend results of Bayer and Gröchenig on localization operators. Furthermore we …
We discuss nonergodic dynamics of interacting spinless fermions in a tilted optical lattice as modeled by XXZ spin chain in magnetic (or electric) field changing linearly across the chain. The time dynamics is studied using exact propagation for small chains and matrix product states techniques for larger system sizes. We consider both the initial Néel separable state as well as the quantum quench scenario in which the initial state may be significantly entangled. We show that the entanglement dynamics is significantly different in both cases. In the former a rapid initial growth is followed b…
We study many-body properties of quantum harmonic oscillator lattices with disorder. A sufficient condition for dynamical localization, expressed as a zero-velocity Lieb-Robinson bound, is formulated in terms of the decay of the eigenfunction correlators for an effective one-particle Hamiltonian. We show how state-of-the-art techniques for proving Anderson localization can be used to prove that these properties hold in a number of standard models. We also derive bounds on the static and dynamic correlation functions at both zero and positive temperature in terms of one-particle eigenfunction c…
We investigate the influence of density, interaction and harmonic confinement on the superfluid to insulator transition (SIT) in disordered fermionic superfluids described by the one-dimensional Hubbard model. We quantify the ground-state single-site entanglement via density-functional theory calculations of the linear entropy. We analyze the critical concentration $C_C$ at which the fully-localized state $-$ a special type of localization, with null entanglement $-$ emerges. We find that $C_C$ is independent on the interaction, but demands a minimum disorder strength to occur. We then derive …
Modular wedge localization, Majorana fields and the Tsirelson limit of the Bell-CHSH inequality
Universidade Federal Rural do Rio de Janeiro（里约热内卢联邦农村大学）；Universidade do Estado do Rio de Janeiro（里约热内卢州立大学）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；ETH Zürich（苏黎世联邦理工学院）
The paper is an extension of quant-ph/9912102. The new framework is tested on the 2-photon spontaneous emission and blackbody radiation. The new effects are rather subtle. The probability of the 2-photon emission is shown to consist of a product of several terms: One which is identical to this from standard quantum optics and the remaining ones formally resembling detector inefficiencies (here arising from nontrivial vacuum structure). The blackbody distribution is indistinguishable from the Planck law for T<T_{critical} but for T>T_{critical} the maximum of the distribution gets lowered and s…
We investigate vacuum entanglement harvesting in the presence of a zero mode. We show that, for a variety of detector models and couplings (namely, Unruh-DeWitt qubit and harmonic oscillator detectors, amplitude and derivative coupling), the results are strongly dependent on the state of the zero mode, revealing an ambiguity in studies of entanglement harvesting with Neumann or periodic boundary conditions, or in general in spacetimes with toroidal topologies.
We study the phenomenon of localization and delocalization in a circuit-QED network with connectivity varying from finite-range to all-to-all coupling. We find a fascinating interplay between interactions and connectivity. In particular, we consider (i) Harmonic (ii) Jaynes-Cummings and (iii) Bose-Hubbard networks. We start with the initial condition where one of the nodes in the network is populated and then let it evolve in time. The time dynamics and steady state characterize the features of localization (self-trapping) in these large-scale networks. For the case of Harmonic networks, exact…
Using the conformal equivalence of translational KMS states on chiral theories with dilational KMS states obtained from restricting the vacuum state to an interval (the chiral inversion of the Unruh-effect) it was shown in a previous publications that the diverging volume (length) factor of the thermodynamic limit corresponds to the logarithmic increase in the attenuation length of the localization-caused vacuum polarization cloud near the causal boundary. This is not a coincidence but rather a structural consequence of the fact that both operator algebras are of the same unique von Neumann ty…
