Exact Solution of a Time-Dependent Quantum Harmonic Oscillator with Two Frequency Jumps via the Lewis–Riesenfeld Dynamical Invariant Method

Coelho, Stanley S; Queiroz, Lucas; Alves, Danilo T.

doi:10.3390/e24121851

Cited by 9 publications

(6 citation statements)

References 58 publications

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“…This is a direct consequence of equations (44) and (45). The equations (41)-( 45) generalize, for a generic intermediary frequency ω int (t) and a final frequency ω f , the results found in [61] for the particular case where ω int (t) = ω 1 and ω f = ω 0 .…”

Section: Squeezing Parameter and Related Quantities For T > τsupporting

confidence: 56%

“…, even when the initial and final frequencies are the same (ω f = ω 0 ) [61]. The argument is similar for ( )…”

Section: Squeezing Parameter and Related Quantities For T > τmentioning

confidence: 60%

“…In [40], Janszky and Yushin showed that these jumps create squeezed states (see also [41][42][43][44][45][46][47][48][49][50][51]). While this procedure is still widely used [52][53][54][55][56][57][58][59][60][61], it is worth noting that sudden jumps in frequency are not the only way to create squeezed states in TDHOs. For example, in [62][63][64][65][66][67], it is shown that squeezing will be generated even for smoothly varying time-dependent frequencies.…”

Section: Introductionmentioning

confidence: 99%

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Squeezing equivalence of quantum harmonic oscillators under different frequency modulations

S Coelho,

Queiroz,

Alves

2024

Phys. Scr.

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The papers by Janszky and Adam [Phys. Rev. A 46, 6091 (1992)] and Chen et al [Phys. Rev. Lett. 104, 063 002 (2010)] are examples of works where one can find the following equivalences: quantum harmonic oscillators subjected to different time-dependent frequency modulations, during a certain time interval τ, exhibit exactly the same final null squeezing parameter (r f = 0). In the present paper, we discuss a more general case of squeezing equivalence, where the final squeezing parameter can be non-null (r f ≥ 0). We show that when the interest is in controlling the forms of the frequency modulations, but keeping free the choice of the values of r f and τ, this in general demands numerical calculations to find these values leading to squeezing equivalences (a particular case of this procedure recovers the equivalence found by Jansky and Adams). On the other hand, when the interest is not in previously controlling the form of these frequencies, but rather r f and τ (and also some constraints, such as minimization of energy), one can have analytical solutions for these frequencies leading to squeezing equivalences (particular cases of this procedure are usually applied in problems of shortcuts to adiabaticity, as done by Chen et al). In this way, this more general squeezing equivalence discussed here is connected to recent and important topics in the literature as, for instance, generation of squeezed states and the obtaining of shortcuts to adiabaticity.

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Section: Squeezing Parameter and Related Quantities For T > τsupporting

confidence: 56%

“…, even when the initial and final frequencies are the same (ω f = ω 0 ) [61]. The argument is similar for ( )…”

Section: Squeezing Parameter and Related Quantities For T > τmentioning

confidence: 60%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Squeezing equivalence of quantum harmonic oscillators under different frequency modulations

S Coelho,

Queiroz,

Alves

2024

Phys. Scr.

Self Cite

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“…In ref. [40], it has been shown that for the particular case 25), one can obtain the effective evolution as…”

Section: The Lewis-riesenfeld Approach and The Ermakov Equationmentioning

confidence: 99%

Adiabatic Shortcuts Completion in Quantum Field Theory: Annihilation of Created Particles

Del Grosso,

Lombardo,

Mazzitelli

et al. 2023

Entropy

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Shortcuts to adiabaticity (STA) are relevant in the context of quantum systems, particularly regarding their control when they are subjected to time-dependent external conditions. In this paper, we investigate the completion of a nonadiabatic evolution into a shortcut to adiabaticity for a quantum field confined within a one-dimensional cavity containing two movable mirrors. Expanding upon our prior research, we characterize the field’s state using two Moore functions that enables us to apply reverse engineering techniques in constructing the STA. Regardless of the initial evolution, we achieve a smooth extension of the Moore functions that implements the STA. This extension facilitates the computation of the mirrors’ trajectories based on the aforementioned functions. Additionally, we draw attention to the existence of a comparable problem within nonrelativistic quantum mechanics.

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“…Existing theoretical literature on driven harmonic oscillators using a Lie algebraic approach often focus on abrupt or adiabatic changes in the parameters of the system in order to approximate its dynamics taking advantage of time-independent solutions [23][24][25][26]. We are interested in the time-dependent driven QHO from a Lie theory point of view that provides a framework to optimize state engineering at any given rate of change without resorting to approximations.…”

Section: Introductionmentioning

confidence: 99%

Continuous-time quantum harmonic oscillator state engineering

García Herrera,

Torres-Leal,

Rodríguez-Lara

2023

New J. Phys.

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The center of mass motion of trapped ions and neutral atoms is suitable for approximation by a time-dependent driven quantum harmonic oscillator whose frequency and driving strength may be controlled with high precision. We show the time evolution for these systems with continuous differentiable time-dependent parameters in terms of the three basic operations provided by its underlying symmetry, rotation, displacement, and squeezing, using a Lie algebraic approach. Our factorization of the dynamics allows for the intuitive construction of protocols for state engineering, for example, creating and removing displacement and squeezing, as well as their combinations, optimizing squeezing, or more complex protocols that work for slow and fast rates of change in the oscillator parameters.

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Exact Solution of a Time-Dependent Quantum Harmonic Oscillator with Two Frequency Jumps via the Lewis–Riesenfeld Dynamical Invariant Method

Cited by 9 publications

References 58 publications

Squeezing equivalence of quantum harmonic oscillators under different frequency modulations

Squeezing equivalence of quantum harmonic oscillators under different frequency modulations

Adiabatic Shortcuts Completion in Quantum Field Theory: Annihilation of Created Particles

Continuous-time quantum harmonic oscillator state engineering

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