Squeezed states in the presence of a time-dependent magnetic field

Jannussis, A.; Vlahos, E.; Skaltsas, D.; Kliros, George S.; Bartzis, V.

doi:10.1007/bf02742825

Cited by 13 publications

(7 citation statements)

References 13 publications

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“…The squeezed states of a free charged particle moving under the homogeneous magnetic field (with the circular gauge of the vector potential) were considered by several authors [16,30,31], but they calculated the squeezing coefficients with respect to the canonical pairs of variables, such as x, p x and y, p y , whose physical meaning is not quite clear. Therefore, it was suggested in [32][33][34] to analyze the variances in the pairs (X, Y) and (ξ, η).…”

Section: Generation Of Squeezingmentioning

confidence: 99%

A Quantum Charged Particle under Sudden Jumps of the Magnetic Field and Shape of Non-Circular Solenoids

Dodonov

Horovits

2019

Quantum Reports

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We consider a quantum charged particle moving in the x y plane under the action of a time-dependent magnetic field described by means of the linear vector potential of the form A = B ( t ) − y ( 1 + β ) , x ( 1 − β ) / 2 . Such potentials with β ≠ 0 exist inside infinite solenoids with non-circular cross sections. The systems with different values of β are not equivalent for nonstationary magnetic fields or time-dependent parameters β ( t ) , due to different structures of induced electric fields. Using the approximation of the stepwise variations of parameters, we obtain explicit formulas describing the change of the mean energy and magnetic moment. The generation of squeezing with respect to the relative and guiding center coordinates is also studied. The change of magnetic moment can be twice bigger for the Landau gauge than for the circular gauge, and this change can happen without any change of the angular momentum. A strong amplification of the magnetic moment can happen even for rapidly decreasing magnetic fields.

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Section: Generation Of Squeezingmentioning

confidence: 99%

A Quantum Charged Particle under Sudden Jumps of the Magnetic Field and Shape of Non-Circular Solenoids

Dodonov

Horovits

2019

Quantum Reports

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“…Explicit words "squeezed states in the magnetic field" were used, e.g., in papers [81][82][83][84][85][86][87]. Evolution of squeezed states in the presence of a magnetic field was considered in [88].…”

Section: Squeezed States and Gaussian Packetsmentioning

confidence: 99%

“…In many papers [81][82][83][84][85][86][87][88], the squeezing phenomena were considered with respect to the canonical pairs of variables, such as x, px and y, py. However, the physical meaning of the numerous formulas for the variances of these variables is not quite clear.…”

Section: "Geometrical" Squeezed Statesmentioning

confidence: 99%

Coherent states in a magnetic field and their generalizations

Dodonov¹

2017

Preprint

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“…These states were used to calculate the propagators, transition amplitudes and transition probabilities between energy levels corresponding to the initial and final asymptotic magnetic fields. Several other aspects of the problem, where solutions to Equation (3) were used, were considered later, e.g., in papers [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] for α = 0. In particular, the problem of squeezing in the time dependent magnetic field with α = 0 was considered in [14,16,17,19,26] with respect to the canonical pairs of variables.…”

Section: Introductionmentioning

confidence: 99%

“…Several other aspects of the problem, where solutions to Equation (3) were used, were considered later, e.g., in papers [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] for α = 0. In particular, the problem of squeezing in the time dependent magnetic field with α = 0 was considered in [14,16,17,19,26] with respect to the canonical pairs of variables. The tomographic approach was used in papers [23,24].…”

Section: Introductionmentioning

confidence: 99%

Energy and Magnetic Moment of a Quantum Charged Particle in Time-Dependent Magnetic and Electric Fields of Circular and Plane Solenoids

Dodonov

Horovits

2021

Entropy

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We consider a quantum spinless nonrelativistic charged particle moving in the xy plane under the action of a time-dependent magnetic field, described by means of the linear vector potential A=B(t)−y(1+α),x(1−α)/2, with two fixed values of the gauge parameter α: α=0 (the circular gauge) and α=1 (the Landau gauge). While the magnetic field is the same in all the cases, the systems with different values of the gauge parameter are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are circles for α=0 and straight lines for α=1. We derive general formulas for the time-dependent mean values of the energy and magnetic moment, as well as for their variances, for an arbitrary function B(t). They are expressed in terms of solutions to the classical equation of motion ε¨+ωα2(t)ε=0, with ω1=2ω0. Explicit results are found in the cases of the sudden jump of magnetic field, the parametric resonance, the adiabatic evolution, and for several specific functions B(t), when solutions can be expressed in terms of elementary or hypergeometric functions. These examples show that the evolution of the mentioned mean values can be rather different for the two gauges, if the evolution is not adiabatic. It appears that the adiabatic approximation fails when the magnetic field goes to zero. Moreover, the sudden jump approximation can fail in this case as well. The case of a slowly varying field changing its sign seems especially interesting. In all the cases, fluctuations of the magnetic moment are very strong, frequently exceeding the square of the mean value.

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Squeezed states in the presence of a time-dependent magnetic field

Cited by 13 publications

References 13 publications

A Quantum Charged Particle under Sudden Jumps of the Magnetic Field and Shape of Non-Circular Solenoids

A Quantum Charged Particle under Sudden Jumps of the Magnetic Field and Shape of Non-Circular Solenoids

Coherent states in a magnetic field and their generalizations

Energy and Magnetic Moment of a Quantum Charged Particle in Time-Dependent Magnetic and Electric Fields of Circular and Plane Solenoids

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