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StatPhys 27 Main Conference

Transient Quantum Processes toward Classical Structure - Through squeezed state and coherent state -

Masahiro Morikawa

Published Apr 18, 2019• 0 citations
OpenAlex

Abstract

Many quantum systems in various fields, a classical signal spontaneously appears without any specific operations/measurements. For example, the initiation of the spontaneous symmetry breaking, the appearance of the off-diagonal long-range order in the Bose-Einstein condensate, the transient process of the quantum fluctuations in the early Universe, etc.  We are interested in the basic principle of these transient processes in quantum systems which shows classical signal spontaneously. We start our observation that some instability often promotes the squeezing of the original quantum system. This is usually interpreted as the particle production or the Bogoliubov shift of the vacuum. At this stage, everything is Unitary and reversible. For example, Hawking radiation around the Black Hole, the thermal state associated with the accelerated observer (Unruh effect), and the particle production in the expanding universe, etc. are all in this category. By using the Schwinger-Keldysh in-in formalism of quantum field theory, we find that these squeezed states are associated with non-dissipative classical fluctuations. We call them dry-noise. Then applying the generalized effective action method and deriving the Langevin equation, we find that these dry-noise triggers, through nonlinear interactions, to develop the coherent state which can be classical if sufficiently developed. This is the origin of the classical signal in the full quantum systems. The appearance of the squeezed state through the tachyonic instability and the development of the coherent state through the nonlinearity seem to be a general transient process that a classical signal spontaneously develops. These states appear more generally not only in the quantum optics. We finally show that this formalism is widely applicable; initiation dynamics of the spontaneous symmetry breaking in quantum systems such as BEC, Black hole entropy, Unruh detectors, and quantum cosmology. These analyses may give some implications on the origin of the irreversibility associated with the transition from quantum to classical. The detail description is in arxiv.org/abs/1810.11293 and the references therein.

Related papers

Transient Dynamics from Quantum to Classical- From the Developed Coherent State via Extreme Squeezing -

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We explore the transient dynamics associated with the emergence of the classical signal in the full quantum system. We start our study from the instability which promotes the squeezing of the quantum system. This is often interpreted as the particle production though being reversible in time. We associate this state a non-dissipative classical fluctuations and study their trigger to develop the coherent state which can be classical if sufficiently developed. The Schwinger-Keldysh in-in formalism yields the classical Langevin equation including the fluctuation force which faithfully reflects the particle production property of the original quantum system. This formalism is applied to some transient process; the initiation of the spontaneous symmetry breaking, appearance of the off-diagonal long-range order in Bose-Einstein condensation, a transient process of the classicalization of the quantum fluctuations in the inflationary cosmology,... and gives some implications on the origin of the irreversibility associated with the transition from quantum to classical.

arXiv:1810.11293•Oct 26, 2018•0 citations

Bose-Einstein condensate collapse and dynamical squeezing of vacuum fluctuations

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We analyze the phenomena of condensate collapse, as described by Donley et al. [Nature 412, 295 (2001)] and N. Claussen [Ph. D thesis, University of Colorado, 2003 (unpublished)] by focusing on the behavior of excitations or fluctuations above the condensate, as driven by the dynamics of the condensate, rather than the dynamics of the condensate alone or the kinetics of the atoms. The dynamics of the condensate squeezes and amplifies the quantum excitations, mixing the positive and negative frequency components of their wave functions thereby creating particles that appear as bursts and jets. By analyzing the changing amplitude and particle content of these excitations, our simple physical picture explains well the overall features of the collapse phenomena and provides excellent quantitative fits with experimental data on several aspects, such as the scaling behavior of the collapse time and the number of particles in the jet. The prediction of the bursts at this level of approximation is less than satisfactory but may be improved by including the backreaction of the excitations on the condensate. The mechanism behind the dominant effect---parametric amplification of vacuum fluctuations and freezing of modes outside of horizon---is similar to that of cosmological particle creation and structure formation in a rapid quench (which is fundamentally different from Hawking radiation in black holes). This shows that Bose-Einstein condensate dynamics is a promising venue for doing ``laboratory cosmology.''

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The concept of coherent states for a quantum system has been generalized in many different ways. One elegant way is the dynamical group approach. The subject of this thesis is the physical application of some dynamical group methods in quantum optics and Bose-Einstein Condensation(BEC) and their use in generalizing some quantum optical states and BEC states. We start by generalizing squeezed coherent states to the displaced squeezed phase number states and studying the signal-to-quantum noise ratio for these states. Following a review of the properties of Kerr states and the basic theory of the deformation of the boson algebra, we present an algebraic approach to Kerr states and generalize them to the squeezed states of the q-parametrized harmonic oscillator. Using the eigenstates of a nonlinear density-dependent annihilation operator of the deformed boson algebra, we propose general time covariant coherent states for any time-independent quantum system. Using the ladder operator approach similar to that of binomial states, we construct interpolating number-coherent states, intermediate states which are generalizations of some fundamental states in quantum optics. Salient statistical properties and non-classical features of these interpolating numbercoherent states are investigated and the interaction with an atomic system in the framework of the Jaynes-Cummings model and the scheme to produce these states are also studied in detail. After briefly reviewing the realization of Bose-Einstein Condensates and relevant theoretical research using mean-field theory, we present a dynamical group approach to Bose-Einstein condensation and the atomic tunnelling between two condensates which interact via a minimal coupling term. First we consider the spectrum of one Bose-Einstein condensate and show that the mean-field dynamics is characterised by the semi-direct product of the 8U(1,1) and Heisenberg-Weyl groups.We then construct a generalized version of the BEC ground states and weakly excited states. It is shown that our states for BEC provide better fits to the experimental results. Then we investigate the tunnelling between the excitations in two condensates which interact via a minimal coupling term. The dynamics of the two interacting Bose systems is characterised by the 80(3,2) group, which leads to an exactly solvable model. Further we describe the dynamics of the tunnelling of the two coupled condensates in terms of the semi-direct product of 80(3,2) and two independent Heisenberg-Weyl groups. From this we obtain the energy spectrum and eigenstates for the two interacting Bose-Einstein condensates, as well as the Josephson current between the two coupled condensates.

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Quantized Fields and Coherent States

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Chapter 6 transforms the optical wave into a quantized form. The electric field is pictured as an infinite ladder of discrete states: this structure allows optical interactions to be described photon by photon. The origin of spontaneous emission emerges as a transition process that is stimulated by electric field fluctuations of the vacuum; Weisskopf–Wigner theory explains why it is irreversible. Squeezed states are introduced and qualitatively unique properties are identified. Statistical analysis of light fields serves as a basis for more quantitative comparisons of fields and their noise properties. Methods of calculating the first and second degrees of coherence are presented. The ranges of values corresponding to “classical” versus “quantum” light sources are discussed. The reduced density matrix is developed to justify analysis that focuses on a subset of the components or dynamics of a complex system, ignoring aspects that are not of primary interest. The problem of calculating the fluorescence spectrum of resonantly excited two-level atoms is considered using both a method of moments and dressed atom theory.

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We clarify the way in which cosmological perturbations of quantum origin, produced during inflation, assume classical properties. Two features play an important role in this process: First, the dynamics of fluctuations which are presently on large cosmological scales leads to a very peculiar state (highly squeezed) that is indistinguishable, in a precise sense, from a classical stochastic process. This holds for almost all initial quantum states. Second, the process of decoherence by interaction with the environment distinguishes the field amplitude basis as the robust pointer basis. We discuss in detail the interplay between these features and use simple analogies such as the free quantum particle to illustrate the main conceptual issues.

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A quasi-particle picture for entanglement cones and horizons in analogue cosmology

Carlos Fulgado-Claudio, A. Bermúdez

Although particle production in curved quantum field theories (cQFTs) is key to our understanding of the early universe and black hole physics, its direct observation requires extreme conditions or unrealistic sensitivities. Recent progress in quantum simulators indicates that analogues of cosmological particle production can be observed in table-top experiments of cold atomic gases described by effective cQFTs. This promises a high degree of tunability in the synthesised curved spacetimes and, moreover, sets a clear roadmap to explore the interplay of particle production with other non-perturbative effects genuine to interacting QFTs. We hereby focus on the appearance of scalar and pseudo-scalar condensates for self-interacting Dirac fermions, and study how dynamical mass generation and spontaneous symmetry breaking affects real-time dynamics through the lens of entanglement. We use the entanglement contour (EC) to analyse the spatio-temporal structure of particle production, showing that a quasi-particle picture for the EC captures the cosmological horizon in accelerating spacetimes, while also being sensitive to the effect of different symmetry-breaking processes. In particular, we show that the combined breakdown of time-reversal symmetry due to the expanding spacetime, and parity due to a pseudo-scalar condensate, manifests through the structure of the light-cone-like propagation of entanglement.

arXiv:2503.19183•Mar 24, 2025•0 citations
Many quantum systems in various fields, a classical signal spontaneously appears without any specific operations/measurements. For example, the initiation of the spontaneous symmetry breaking, the appearance of the off-diagonal long-range order in the Bose-Einstein condensate, the transient process of the quantum fluctuations in the early Universe, etc.  We are interested in the basic principle of these transient processes in quantum systems which shows classical signal spontaneously. We start our observation that some instability often promotes the squeezing of the original quantum system. This is usually interpreted as the particle production or the Bogoliubov shift of the vacuum. At this stage, everything is Unitary and reversible. For example, Hawking radiation around the Black Hole, the thermal state associated with the accelerated observer (Unruh effect), and the particle production in the expanding universe, etc. are all in this category. By using the Schwinger-Keldysh in-in formalism of quantum field theory, we find that these squeezed states are associated with non-dissipative classical fluctuations. We call them dry-noise. Then applying the generalized effective action method and deriving the Langevin equation, we find that these dry-noise triggers, through nonlinear interactions, to develop the coherent state which can be classical if sufficiently developed. This is the origin of the classical signal in the full quantum systems. The appearance of the squeezed state through the tachyonic instability and the development of the coherent state through the nonlinearity seem to be a general transient process that a classical signal spontaneously develops. These states appear more generally not only in the quantum optics. We finally show that this formalism is widely applicable; initiation dynamics of the spontaneous symmetry breaking in quantum systems such as BEC, Black hole entropy, Unruh detectors, and quantum cosmology. These analyses may give some implications on the origin of the irreversibility associated with the transition from quantum to classical. The detail description is in arxiv.org/abs/1810.11293 and the references therein.
We explore the transient dynamics associated with the emergence of the classical signal in the full quantum system. We start our study from the instability which promotes the squeezing of the quantum system. This is often interpreted as the particle production though being reversible in time. We associate this state a non-dissipative classical fluctuations and study their trigger to develop the coherent state which can be classical if sufficiently developed. The Schwinger-Keldysh in-in formalism yields the classical Langevin equation including the fluctuation force which faithfully reflects the particle production property of the original quantum system. This formalism is applied to some transient process; the initiation of the spontaneous symmetry breaking, appearance of the off-diagonal long-range order in Bose-Einstein condensation, a transient process of the classicalization of the quantum fluctuations in the inflationary cosmology,... and gives some implications on the origin of the irreversibility associated with the transition from quantum to classical.
We analyze the phenomena of condensate collapse, as described by Donley et al. [Nature 412, 295 (2001)] and N. Claussen [Ph. D thesis, University of Colorado, 2003 (unpublished)] by focusing on the behavior of excitations or fluctuations above the condensate, as driven by the dynamics of the condensate, rather than the dynamics of the condensate alone or the kinetics of the atoms. The dynamics of the condensate squeezes and amplifies the quantum excitations, mixing the positive and negative frequency components of their wave functions thereby creating particles that appear as bursts and jets. By analyzing the changing amplitude and particle content of these excitations, our simple physical picture explains well the overall features of the collapse phenomena and provides excellent quantitative fits with experimental data on several aspects, such as the scaling behavior of the collapse time and the number of particles in the jet. The prediction of the bursts at this level of approximation is less than satisfactory but may be improved by including the backreaction of the excitations on the condensate. The mechanism behind the dominant effect---parametric amplification of vacuum fluctuations and freezing of modes outside of horizon---is similar to that of cosmological particle creation and structure formation in a rapid quench (which is fundamentally different from Hawking radiation in black holes). This shows that Bose-Einstein condensate dynamics is a promising venue for doing ``laboratory cosmology.''
The concept of coherent states for a quantum system has been generalized in many different ways. One elegant way is the dynamical group approach. The subject of this thesis is the physical application of some dynamical group methods in quantum optics and Bose-Einstein Condensation(BEC) and their use in generalizing some quantum optical states and BEC states. We start by generalizing squeezed coherent states to the displaced squeezed phase number states and studying the signal-to-quantum noise ratio for these states. Following a review of the properties of Kerr states and the basic theory of the deformation of the boson algebra, we present an algebraic approach to Kerr states and generalize them to the squeezed states of the q-parametrized harmonic oscillator. Using the eigenstates of a nonlinear density-dependent annihilation operator of the deformed boson algebra, we propose general time covariant coherent states for any time-independent quantum system. Using the ladder operator approach similar to that of binomial states, we construct interpolating number-coherent states, intermediate states which are generalizations of some fundamental states in quantum optics. Salient statistical properties and non-classical features of these interpolating numbercoherent states are investigated and the interaction with an atomic system in the framework of the Jaynes-Cummings model and the scheme to produce these states are also studied in detail. After briefly reviewing the realization of Bose-Einstein Condensates and relevant theoretical research using mean-field theory, we present a dynamical group approach to Bose-Einstein condensation and the atomic tunnelling between two condensates which interact via a minimal coupling term. First we consider the spectrum of one Bose-Einstein condensate and show that the mean-field dynamics is characterised by the semi-direct product of the 8U(1,1) and Heisenberg-Weyl groups.We then construct a generalized version of the BEC ground states and weakly excited states. It is shown that our states for BEC provide better fits to the experimental results. Then we investigate the tunnelling between the excitations in two condensates which interact via a minimal coupling term. The dynamics of the two interacting Bose systems is characterised by the 80(3,2) group, which leads to an exactly solvable model. Further we describe the dynamics of the tunnelling of the two coupled condensates in terms of the semi-direct product of 80(3,2) and two independent Heisenberg-Weyl groups. From this we obtain the energy spectrum and eigenstates for the two interacting Bose-Einstein condensates, as well as the Josephson current between the two coupled condensates.
Chapter 6 transforms the optical wave into a quantized form. The electric field is pictured as an infinite ladder of discrete states: this structure allows optical interactions to be described photon by photon. The origin of spontaneous emission emerges as a transition process that is stimulated by electric field fluctuations of the vacuum; Weisskopf–Wigner theory explains why it is irreversible. Squeezed states are introduced and qualitatively unique properties are identified. Statistical analysis of light fields serves as a basis for more quantitative comparisons of fields and their noise properties. Methods of calculating the first and second degrees of coherence are presented. The ranges of values corresponding to “classical” versus “quantum” light sources are discussed. The reduced density matrix is developed to justify analysis that focuses on a subset of the components or dynamics of a complex system, ignoring aspects that are not of primary interest. The problem of calculating the fluorescence spectrum of resonantly excited two-level atoms is considered using both a method of moments and dressed atom theory.
We clarify the way in which cosmological perturbations of quantum origin, produced during inflation, assume classical properties. Two features play an important role in this process: First, the dynamics of fluctuations which are presently on large cosmological scales leads to a very peculiar state (highly squeezed) that is indistinguishable, in a precise sense, from a classical stochastic process. This holds for almost all initial quantum states. Second, the process of decoherence by interaction with the environment distinguishes the field amplitude basis as the robust pointer basis. We discuss in detail the interplay between these features and use simple analogies such as the free quantum particle to illustrate the main conceptual issues.
Although particle production in curved quantum field theories (cQFTs) is key to our understanding of the early universe and black hole physics, its direct observation requires extreme conditions or unrealistic sensitivities. Recent progress in quantum simulators indicates that analogues of cosmological particle production can be observed in table-top experiments of cold atomic gases described by effective cQFTs. This promises a high degree of tunability in the synthesised curved spacetimes and, moreover, sets a clear roadmap to explore the interplay of particle production with other non-perturbative effects genuine to interacting QFTs. We hereby focus on the appearance of scalar and pseudo-scalar condensates for self-interacting Dirac fermions, and study how dynamical mass generation and spontaneous symmetry breaking affects real-time dynamics through the lens of entanglement. We use the entanglement contour (EC) to analyse the spatio-temporal structure of particle production, showing that a quasi-particle picture for the EC captures the cosmological horizon in accelerating spacetimes, while also being sensitive to the effect of different symmetry-breaking processes. In particular, we show that the combined breakdown of time-reversal symmetry due to the expanding spacetime, and parity due to a pseudo-scalar condensate, manifests through the structure of the light-cone-like propagation of entanglement.