With the choice of Coulomb gauge, we investigated coherent state and squeezed state of the light propagating through homogeneious conducting linear media with no charge density using quantum results of the LR invariant operator method. We described coherent and squeezed properties of electric and magnetic fields. The fields in coherent and squeezed states are decayed exponentially with time due to the conductivity of the media. We studied probability density of the coherent wave packet and the highly squeezed wave packets. The uncertainty relation between the two orthogonal phase amplitudes, â1 and â2, in coherent state is same as the uncertainty relation in vacuum number state. The envelope of the relative noise in coherent state alternately become large and small with time and position. The uncertainty relation between canonical variables are varied depending on the value of conductivity σ in squeezed state, but not lowered below ħ/2 which is quantum-mechanically acceptable minimum uncertainty.

Coherent and Squeezed States for Light in Homogeneous Conducting Linear Media by an Invariant Operator Method

We investigated coherent and squeezed states of light in linear media whose parameters are explicitly dependent on time by making use of the Lewis–Riesenfeld invariant operator method. Not only the field strengths but also the fluctuations of the fields both in coherent and in squeezed states are decayed with time. The relative noise of the field strengths are calculated in coherent state. Quantum statistical properties of the chaotic field are investigated. We applied our theory to a phenomenological model of the biophoton system and compared the corresponding result of the uncertainty product with that obtained from a previous report.

http://iopscience.iop.org/article/10.1088/0953-4075/39/3/019/pdf

Coherent and squeezed states of light in linear media with time-dependent parameters by Lewis–Riesenfeld invariant operator method

Exact quantum states of the time-dependent quadratic Hamiltonian system are investigated using SU(1,1) Lie algebra. We realized SU(1,1) Lie algebra by defining appropriate SU(1,1) generators and derived exact wave functions using this algebra for the system. Raising and lowering operators of SU(1,1) Lie algebra expressed by multiplying a time-constant magnitude and a time-dependent phase factor. Two kinds of the SU(1,1) coherent states, i.e., even and odd coherent states and Perelomov coherent states are studied. We applied our result to the Caldirola–Kanai oscillator. The probability density of these coherent states for the Caldirola–Kanai oscillator converged to the center as time goes by, due to the damping constant γ. All the coherent state probability densities for the driven system are somewhat deformed.

SU(1,1) Lie Algebra Applied to the General Time-dependent Quadratic Hamiltonian System

By means of a two-step unitary transformation, the exact quantum mechanical solution of two-dimensional mesoscopic circuit coupled via inductance is derived. The wavefunction, propagator and expectation value of Hamiltonian are evaluated. The fluctuations of charges and currents are calculated and uncertainty products between charges and their conjugate currents are obtained. We apply our results to the system with special cases of the power source such as the sinusoidal and the sawtooth power source and show that the probability densities oscillate with time due to the power source.

http://iopscience.iop.org/article/10.1088/0031-8949/73/6/010/pdf

Exact solution of a quantized LC circuit coupled to a power source

We introduce exactly solvable quantum parametric oscillators, which are generalizations of the quantum problems related with the classical orthogonal polynomials of Hermite, Laguerre, and Jacobi type, introduced in the work of Buyukasik et al. [J. Math. Phys. 50, 072102 (2009)]. Quantization of these models with specific damping, frequency, and external forces is obtained using the Wei-Norman Lie algebraic approach. This determines the evolution operator exactly in terms of two linearly independent homogeneous solutions and a particular solution of the corresponding classical equation of motion. Then, time-evolution of wave functions and coherent states are found explicitly. Probability densities, expectation values, and uncertainty relations are evaluated and their properties are investigated under the influence of the external terms.

/pdf/exactly-solvable-hermite-laguerre-and-jacobi-type-quantum-4ghpr8a5wd.pdf

Exactly solvable Hermite, Laguerre, and Jacobi type quantum parametric oscillators

By introducing an invariant operator, we obtain exact wave functions for a general time-dependent quadratic harmonic oscillator. The coherent states, both inx- andp-spaces, are calculated. We confirm that the uncertainty product in coherent state is always larger thankh/2 and is equal to the minimum of the uncertainty product of the number states. The displaced wave packet for Caldirola-Kanai oscillator in coherent state oscillates back and forth with time about the center as for a classical oscillator. The amplitude of oscillation with no driving force decreases due to the dissipation in the system. However, the oscillation with resonant frequency oscillates with a large amplitude, even after a sufficient time elapse.

Jeong Ryeol Choi

Papers

Coherent states of general time-dependent harmonic oscillator