Exact manipulations to Bloch states of a particle in a double cosine potential

Kuo, Hao‐Chung; Wang, Hai; Chen, Qiong

doi:10.1016/j.physleta.2007.03.042

Cited by 6 publications

(6 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The lowest order approximation to the ion trajectory can only be identical to the solution found by the pseudopotential approximation [29] in the weak-field case with small strengths [5], |a x |, q 2 1 1. For the case q 2 = 0, equation (3) mathematically agrees with the time-independent Schrödinger equation with a double-cosine potential [28]. If the system matches the restriction relations among a x , q 1 and q 2 ,…”

Section: Exact Classical Solutions Of the Simple Formsmentioning

confidence: 60%

“…from a Riccati transformation, we can construct the simple exact solutions [28] x c = ϕ 1 = A 1 e − q 1 4 cos 2t sin t (5) and…”

Section: Exact Classical Solutions Of the Simple Formsmentioning

confidence: 99%

“…On the other hand, previous research revealed that two-or multi-frequency driving has found a variety of applications in exploring quantum tunneling and the related control [23][24][25][26][27]. The simple exact solutions of the time-independent Schrödinger equation with a double-cosine potential were constructed in our previous work [28], which provided the possibility of generating simple exact solutions of the classical Mathieu equation with double-rf driving. Because quantum motions of the system may be associated with the simple classical solutions, and double-rf driving consisting of two periodic fields could be realized in experiments, we can suggest an analytical scheme for manipulating nonstationary motional states of the trapped ion more accurately.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum control of a Paul-trapped ion via double radio-frequency driving

Chen¹,

Kuo²,

Wang³

2010

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

Due to an infinite series solution of the classical Mathieu equation, using single-radio-frequency (rf) driving makes it difficult to manipulate motional states of a Paul-trapped ion. Here, we apply double-rf driving consisting of two external fields to generate the squeezed coherent states of simple forms. Stability parameter regions of the system are found in which both the first and second rf fields may be very strong but only the latter can be weak. Based on exact solutions, we investigate the time evolutions of expectation energies and controllable transitions between not only two stationary states, but also two nonstationary states. Such a quantum-control scenario may be tested experimentally.

show abstract

Section: Exact Classical Solutions Of the Simple Formsmentioning

confidence: 60%

“…from a Riccati transformation, we can construct the simple exact solutions [28] x c = ϕ 1 = A 1 e − q 1 4 cos 2t sin t (5) and…”

Section: Exact Classical Solutions Of the Simple Formsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum control of a Paul-trapped ion via double radio-frequency driving

Chen¹,

Kuo²,

Wang³

2010

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

show abstract

“…To the best of our knowledge, these have not been investigated to date. The double cosine potential [53] that we have taken is…”

Section: Implementation Of Ham In Selected Problemsmentioning

confidence: 99%

Homotopy Analysis Method and Time-fractional NLSE with Double Cosine, Morse, and New Hyperbolic Potential Traps

Ghosh¹,

Das²,

Sarkar³

2022

Nelin. Dinam.

View full text Add to dashboard Cite

A brief outline of the derivation of the time-fractional nonlinear Schrödinger equation (NLSE) is furnished. The homotopy analysis method (HAM) is applied to study time-fractional NLSE with three separate trapping potential models that we believe have not been investigated yet. The first potential is a double cosine potential $[V(x)=V_{1}\cos x+V_{2}\cos 2x]$, the second one is the Morse potential $[V(x)=V_{1}e^{-2\beta x}+V_{2}e^{-\beta x}]$, and a hyperbolic potential $[V(x)=V_{0}\tanh(x)\sech(x)]$ is taken as the third model. The fractional derivatives and integrals are described in the Caputo and Riemann Liouville sense, respectively. The solutions are given in the form of convergent series with easily computable components. A physical analysis with graphical representations explicitly reveals that HAM is effective and convenient for solving nonlinear differential equations of fractional order.

show abstract

“…The quantum motion of an electron driven by a strong time-dependent linear potential in a 1D quantum wire has been investigated and interesting physical properties studied [13]. The possibility of exactly manipulating the quantum motional states of a single particle held in a double cosine potential by using laser beams has been explored [14].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Particle in Confined-Harmonic Potential in External Static Electric Field and Strong Laser Field

Lumb¹,

Prasad²

2013

JMP

View full text Add to dashboard Cite

Dynamics of a particle in confined-harmonic potential, subjected to external static electric and time-dependent laser fields is studied. The energy levels and wave functions of unperturbed harmonic oscillator are evaluated using B-polynomial Galerkin method. Matrix formulation is used throughout the procedure. This procedure is very simple and efficient in comparison with other methods. Modifications of wave functions and energy levels due to static electric field are also calculated. Finally, absorption spectra of such a driven oscillator are studied and explained.

show abstract

Exact manipulations to Bloch states of a particle in a double cosine potential

Cited by 6 publications

References 27 publications

Quantum control of a Paul-trapped ion via double radio-frequency driving

Quantum control of a Paul-trapped ion via double radio-frequency driving

Homotopy Analysis Method and Time-fractional NLSE with Double Cosine, Morse, and New Hyperbolic Potential Traps

Dynamics of Particle in Confined-Harmonic Potential in External Static Electric Field and Strong Laser Field

Contact Info

Product

Resources

About