## Time Evolution

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### Hongyi Fan - One of the best experts on this subject based on the ideXlab platform.

• ##### parametric amplifier studied as Time Evolution of angular momentum system in entangled state representation
International Journal of Theoretical Physics, 2015
Co-Authors: Hongyi Fan
Abstract:

We present a new approach for studying theoretical model of a parametric amplifier. We show that Time-Evolution of parametric amplifier can be treated as formalism of angular momentum system by using the newly found bosonic operator realization of three generators (J +, J −, J z ). The entangled state representation is essential in this approach. The transition probability from vacuum state to two-mode squeezed state in a parametric amplifier can be directly evaluated.

• ##### Time Evolution of wigner functions governed by bipartite hamiltonian system with kinetic coupling
Brazilian Journal of Physics, 2010
Co-Authors: Qiuyu Liu, Hongchun Yuan, Hongyi Fan
Abstract:

For the bipartite Hamiltonian system with kinetic coupling, we derive Time Evolution equation of Wigner functions by virtue of the bipartite entangled state representation and entangled Wigner operator, which just indicates that choosing a good representation indeed provides great convenience for us to deal with the dynamics problem.

• ##### Time Evolution of wigner function in laser process derived by entangled state representation
Optics Communications, 2009
Co-Authors: Hongyi Fan
Abstract:

Evaluating the Wigner function of quantum states in the entangled state representation is introduced, based on which we present a new approach for deriving Time Evolution formula of Wigner function in laser process. Application of this formula to photon number measurement in laser process is also presented, as an example, the case when the initial state is a photon-added coherent state is discussed.

• ##### Time Evolution of the wigner function in the entangled state representation
Physical Review A, 2002
Co-Authors: Hongyi Fan
Abstract:

For quantum-mechanical entangled states we introduce the entangled Wigner operator in the entangled-state representation. We derive the Time Evolution equation of the entangled Wigner operator. The trace product rule for entangled Wigner functions is also obtained.

### H J Carmichael - One of the best experts on this subject based on the ideXlab platform.

• ##### quantum state reduction and conditional Time Evolution of wave particle correlations in cavity qed
Physical Review Letters, 2000
Co-Authors: G T Foster, L A Orozco, H M Castrobeltran, H J Carmichael
Abstract:

We report measurements in cavity QED of a wave-particle correlation function which records the conditional Time Evolution of the field of a fraction of a photon. Detection of a photon prepares a state of well-defined phase that evolves back to equilibrium via a damped vacuum Rabi oscillation. We record the regression of the field amplitude. The recorded correlation function is nonclassical and provides an efficiency independent path to the spectrum of squeezing. Nonclassicality is observed even when the intensity fluctuations are classical. PACS numbers: 42.50.Dv, 32.80. ‐ t, 42.50.Ct The seminal work of Hanbury-Brown and Twiss [1] marks the beginning of the systematic study of the quantum fluctuations of light. Two lines of experiments are notable: those measuring correlations between pairs of photodetections (particle aspect of light) [2‐6] and squeezing experiments which measure the variance of the electromagnetic field amplitude (wave aspect of light) [7‐9]. No attempt has been made previously to draw the particle and wave aspects together by correlating a photon detection with fluctuations of the electromagnetic field amplitude. We have done this, extending the ideas of Hanbury-Brown and Twiss to record the conditional Time Evolution of the amplitude fluctuations of an electromagnetic wave. Measurements are made in the strong-coupling regime of cavity quantum electrodynamics (QED) [10] and exhibit the nonclassical fluctuations of light in a dramatic new way.

• ##### quantum state reduction and conditional Time Evolution of wave particle correlations in cavity qed
Physical Review Letters, 2000
Co-Authors: G T Foster, L A Orozco, H M Castrobeltran, H J Carmichael
Abstract:

We report measurements in cavity QED of a wave-particle correlation function which records the conditional Time Evolution of the field of a fraction of a photon. Detection of a photon prepares a state of well-defined phase that evolves back to equilibrium via a damped vacuum Rabi oscillation. We record the regression of the field amplitude. The recorded correlation function is nonclassical and provides an efficiency independent path to the spectrum of squeezing. Nonclassicality is observed even when the intensity fluctuations are classical.

### Philip D Mannheim - One of the best experts on this subject based on the ideXlab platform.

• ##### pt symmetry as a necessary and sufficient condition for unitary Time Evolution
Philosophical Transactions of the Royal Society A, 2013
Co-Authors: Philip D Mannheim
Abstract:

While Hermiticity of a Time-independent Hamiltonian leads to unitary Time Evolution, in and of itself, the requirement of Hermiticity is only sufficient for unitary Time Evolution. In this paper, w...

• ##### pt symmetry as a necessary and sufficient condition for unitary Time Evolution
arXiv: High Energy Physics - Theory, 2009
Co-Authors: Philip D Mannheim
Abstract:

While Hermiticity of a Time-independent Hamiltonian leads to unitary Time Evolution, in and of itself, the requirement of Hermiticity is only sufficient for unitary Time Evolution. In this paper we provide conditions that are both necessary and sufficient. We show that $PT$ symmetry of a Time-independent Hamiltonian, or equivalently, reality of the secular equation that determines its eigenvalues, is both necessary and sufficient for unitary Time Evolution. For any $PT$-symmetric Hamiltonian $H$ there always exists an operator $V$ that relates $H$ to its Hermitian adjoint according to $VHV^{-1}=H^{\dagger}$. When the energy spectrum of $H$ is complete, Hilbert space norms  constructed with this $V$ are always preserved in Time. With the energy eigenvalues of a real secular equation being either real or appearing in complex conjugate pairs, we thus establish the unitarity of Time Evolution in both cases. We also establish the unitarity of Time Evolution for Hamiltonians whose energy spectra are not complete. We show that when the energy eigenvalues of a Hamiltonian are real and complete the operator $V$ is a positive Hermitian operator, which has an associated square root operator that can be used to bring the Hamiltonian to a Hermitian form. We show that systems with $PT$-symmetric Hamiltonians obey causality. We note that Hermitian theories are ordinarily associated with a path integral quantization prescription in which the path integral measure is real, while in contrast non-Hermitian but $PT$-symmetric theories are ordinarily associated with path integrals in which the measure needs to be complex, but in which the Euclidean Time continuation of the path integral is nonetheless real. We show that through $PT$ symmetry the fourth-order derivative Pais-Uhlenbeck theory can be stabilized against transitions to states negative frequency.

### G T Foster - One of the best experts on this subject based on the ideXlab platform.

• ##### quantum state reduction and conditional Time Evolution of wave particle correlations in cavity qed
Physical Review Letters, 2000
Co-Authors: G T Foster, L A Orozco, H M Castrobeltran, H J Carmichael
Abstract:

We report measurements in cavity QED of a wave-particle correlation function which records the conditional Time Evolution of the field of a fraction of a photon. Detection of a photon prepares a state of well-defined phase that evolves back to equilibrium via a damped vacuum Rabi oscillation. We record the regression of the field amplitude. The recorded correlation function is nonclassical and provides an efficiency independent path to the spectrum of squeezing. Nonclassicality is observed even when the intensity fluctuations are classical. PACS numbers: 42.50.Dv, 32.80. ‐ t, 42.50.Ct The seminal work of Hanbury-Brown and Twiss [1] marks the beginning of the systematic study of the quantum fluctuations of light. Two lines of experiments are notable: those measuring correlations between pairs of photodetections (particle aspect of light) [2‐6] and squeezing experiments which measure the variance of the electromagnetic field amplitude (wave aspect of light) [7‐9]. No attempt has been made previously to draw the particle and wave aspects together by correlating a photon detection with fluctuations of the electromagnetic field amplitude. We have done this, extending the ideas of Hanbury-Brown and Twiss to record the conditional Time Evolution of the amplitude fluctuations of an electromagnetic wave. Measurements are made in the strong-coupling regime of cavity quantum electrodynamics (QED) [10] and exhibit the nonclassical fluctuations of light in a dramatic new way.

• ##### quantum state reduction and conditional Time Evolution of wave particle correlations in cavity qed
Physical Review Letters, 2000
Co-Authors: G T Foster, L A Orozco, H M Castrobeltran, H J Carmichael
Abstract:

We report measurements in cavity QED of a wave-particle correlation function which records the conditional Time Evolution of the field of a fraction of a photon. Detection of a photon prepares a state of well-defined phase that evolves back to equilibrium via a damped vacuum Rabi oscillation. We record the regression of the field amplitude. The recorded correlation function is nonclassical and provides an efficiency independent path to the spectrum of squeezing. Nonclassicality is observed even when the intensity fluctuations are classical.

### L A Orozco - One of the best experts on this subject based on the ideXlab platform.

• ##### quantum state reduction and conditional Time Evolution of wave particle correlations in cavity qed
Physical Review Letters, 2000
Co-Authors: G T Foster, L A Orozco, H M Castrobeltran, H J Carmichael
Abstract:

We report measurements in cavity QED of a wave-particle correlation function which records the conditional Time Evolution of the field of a fraction of a photon. Detection of a photon prepares a state of well-defined phase that evolves back to equilibrium via a damped vacuum Rabi oscillation. We record the regression of the field amplitude. The recorded correlation function is nonclassical and provides an efficiency independent path to the spectrum of squeezing. Nonclassicality is observed even when the intensity fluctuations are classical. PACS numbers: 42.50.Dv, 32.80. ‐ t, 42.50.Ct The seminal work of Hanbury-Brown and Twiss [1] marks the beginning of the systematic study of the quantum fluctuations of light. Two lines of experiments are notable: those measuring correlations between pairs of photodetections (particle aspect of light) [2‐6] and squeezing experiments which measure the variance of the electromagnetic field amplitude (wave aspect of light) [7‐9]. No attempt has been made previously to draw the particle and wave aspects together by correlating a photon detection with fluctuations of the electromagnetic field amplitude. We have done this, extending the ideas of Hanbury-Brown and Twiss to record the conditional Time Evolution of the amplitude fluctuations of an electromagnetic wave. Measurements are made in the strong-coupling regime of cavity quantum electrodynamics (QED) [10] and exhibit the nonclassical fluctuations of light in a dramatic new way.

• ##### quantum state reduction and conditional Time Evolution of wave particle correlations in cavity qed
Physical Review Letters, 2000
Co-Authors: G T Foster, L A Orozco, H M Castrobeltran, H J Carmichael
Abstract:

We report measurements in cavity QED of a wave-particle correlation function which records the conditional Time Evolution of the field of a fraction of a photon. Detection of a photon prepares a state of well-defined phase that evolves back to equilibrium via a damped vacuum Rabi oscillation. We record the regression of the field amplitude. The recorded correlation function is nonclassical and provides an efficiency independent path to the spectrum of squeezing. Nonclassicality is observed even when the intensity fluctuations are classical.