Squeezing of Relative and Center-of-Orbit Coordinates of a Charged Particle by Step-Wise Variations of a Uniform Magnetic Field with an Arbitrary Linear Vector Potential

Dodonov, V. V.; Horovits, M.B.

doi:10.1007/s10946-018-9733-1

Cited by 9 publications

(12 citation statements)

References 34 publications

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“…where B is the strength of the uniform magnetic field inside the solenoid. Comparing (1) with (8), we obtain the relation between parameter β and the semi-axes of the elliptic solenoid:…”

Section: Vector Potential Inside An Infinite Solenoid With An Arbitramentioning

confidence: 99%

“…This can be explained by different geometries of the induced electric field E(r, t) = −∂A(r, t)/∂(ct) (we use the Gaussian system of units). Other manifestations of the nonequivalence between the Landau and circular gauges in the case of time-dependent magnetic fields were observed in studies [7,8] devoted to the problem of generation of squeezed states of charged particles in magnetic fields.…”

Section: Introductionmentioning

confidence: 95%

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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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“…where B is the strength of the uniform magnetic field inside the solenoid. Comparing (1) with (8), we obtain the relation between parameter β and the semi-axes of the elliptic solenoid:…”

Section: Vector Potential Inside An Infinite Solenoid With An Arbitramentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

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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“…Interestingly, this issue was analyzed in the context of squeezing generation in the problem of a charged particle under the influence of a magnetic field in Refs. [62,63]. By assumption, the HO starts in its fundamental state with frequency ω 0 , then, at t = 0, its frequency suddenly increases to ω 1 and, after a finite time interval τ , it comes back to its original value ω 0 .…”

Section: Introductionmentioning

confidence: 98%

A Time-Dependent Harmonic Oscillator with Two Frequency Jumps: an Exact Algebraic Solution

et al. 2020

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We consider a harmonic oscillator (HO) with a time-dependent frequency which undergoes two successive abrupt changes. By assumption, the HO starts in its fundamental state with frequency ω 0 , then, at t = 0, its frequency suddenly increases to ω 1 and, after a finite time interval τ , it comes back to its original value ω 0. Contrary to what one could naively think, this problem is quite a non-trivial one. Using algebraic methods, we obtain its exact analytical solution and show that at any time t > 0 the HO is in a vacuum squeezed state. We compute explicitly the corresponding squeezing parameter (SP) relative to the initial state at an arbitrary instant and show that, surprisingly, it exhibits oscillations after the first frequency jump (from ω 0 to ω 1), remaining constant after the second jump (from ω 1 back to ω 0). We also compute the time evolution of the variance of a quadrature. Last, but not least, we calculate the vacuum (fundamental state) persistence probability amplitude of the HO, as well as its transition probability amplitude for any excited state.

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“…Note that the traces (29) and (30) are invariant with respect to the transformation s → s −1 . Two important special cases will be analyzed in more details in the subsequent Sections.…”

Section: The Circular Gauge: Generalmentioning

confidence: 99%

“…The difference can be clearly seen, if one compares explicit expressions for the propagators and transition amplitudes for the two gauges given in [9,10]. Other manifestations of the gauge nonequivalence in the case of time-dependent magnetic fields were observed in studies [29,30], devoted to the problem of generation of squeezed states of charged particles in magnetic fields, with respect to relative and guiding center coordinates. Clearly, the origin of the gauge nonequivalence is in different spatial distributions of the induced electric field E(r, t) = −∂A(r, t)/∂(ct), whose lines of force are circles for α = 0 (the circular solenoid) and straight lines for α = 1 (the plane solenoid).…”

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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Squeezing of Relative and Center-of-Orbit Coordinates of a Charged Particle by Step-Wise Variations of a Uniform Magnetic Field with an Arbitrary Linear Vector Potential

Cited by 9 publications

References 34 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

A Time-Dependent Harmonic Oscillator with Two Frequency Jumps: an Exact Algebraic Solution

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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