Nonperturbative electron dynamics in crossed fields

Villas‐Bôas, J. M.; Zhang, Wei; Ulloa, Sergio E.; Rivera, P. H.; Studart, Nélson

doi:10.1103/physrevb.66.085325

Cited by 21 publications

(32 citation statements)

References 43 publications

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“…This effect is also known as coherent destruction of tunneling (CDT) 16,17 as, tunneling between one state and the other is destroyed by making unity the probability of staying of the particle in the initial state. So, this question has been recently the main motivation for several works on two-level systems 18,19,20,21 . Some of these papers have put forward an interesting non perturbative result showing a set of curves for the crossing of the quasi-energies of the Floquet solution for two-level systems with different periodical external fields.…”

Section: Quantum Computationmentioning

confidence: 99%

Perturbative results on localization for a driven two-level system

Frasca¹

2003

Phys. Rev. B

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Using perturbation theory in the strong coupling regime, that is, the dual Dyson series, and renormalization group techniques to re-sum secular terms, we obtain the perturbation series of the two-level system driven by a sinusoidal field till second order. The third order correction to the energy levels is obtained proving how this correction does not modify at all the localization condition for a strong field as arising from the zeros of the zero-th Bessel function of integer order. A comparison with weak coupling perturbation theory is done showing how the latter is contained in the strong coupling expansion in the proper limits. The strong coupling expansion we obtain proves to be accurate in the regime of high-frequency driving field. This computation gives an explicit analytical form to Floquet eigenstates and quasi-energies for this problem, for high-frequency driving fields, supporting recent theoretical and experimental findings for quantum devices expected to give a representation for qubits in quantum computation.

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Section: Quantum Computationmentioning

confidence: 99%

Perturbative results on localization for a driven two-level system

Frasca¹

2003

Phys. Rev. B

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“…Since H is periodic in time (H(t) = H(t + τ ), where τ = 2π/ω is the period) we can make use of the standard Floquet theory 7,12 and write the solutions of the time-dependent Schrödinger equation as ψ(t) = exp(−iεt/h)u(t), where u(t), the so-called Floquet state, is also periodic in time with the same period τ , and ε is the Floquet characteristic exponent or quasienergy, which can be obtained from the eigenvalue equation…”

Section: 234mentioning

confidence: 99%

Selective coherent destruction of tunneling in a quantum-dot array

2004

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The coherent manipulation of quantum states is one of the main tasks required in quantum computation. In this paper we demonstrate that it is possible to control coherently the electronic position of a particle in a quantum-dot array. By tuning an external ac electric field we can selectively suppress the tunneling between dots, trapping the particle in a determined region of the array. The problem is treated non-perturbatively by a time-dependent Hamiltonian in the effective mass approximation and using Floquet theory. We find that the quasienergy spectrum exhibits crossings at certain field intensities that result in the selective suppression of tunneling. The search for a solid-state based quantum computer device has attracted a lot of interest in the physics community recently. The ability to manipulate a quantum state and measure it is one of the most important and pressing challenges to be addressed in real implementations. Fortunately great advances in this area have been achieved recently. A good example of that are the Rabi oscillations observed in exciton states of self-assembled quantum dots (QDs). 1,2,3,4Our work here is based on the coherent destruction of tunneling (CDT) of a driven two-level system, 5,6,7 in which the tunneling of one particle in a symmetric double well potential is suppressed for some special value of frequency and field intensity. We propose a system in which one can selectively suppress the tunneling between individual quantum dots tuned by the external ac electric field. This effect provides one with a different experimental handle to control a quantum mechanical system. By suitable variation of the frequency and applied ac field amplitude, one can precise the location of one electron in the multidot array. To demonstrate this effect, our model employs an effective mass nearest-neighbor tight-biding approximation (NNTB).8,9,10 The dynamics is analyzed using Floquet theory and the direct integration of the time-dependent Schrödinger equation.The Hamiltonian for an electron in an array of identical QDs under a strong ac field within NNTB is written as(1) where T e is the hopping matrix element, a † j and a j are, respectively, the electron creation and annihilation operator in the dot j, e is the electronic charge, F is the field intensity, d is the separation between dots, ω is the field frequency, and φ is the phase of the drive field. This phase, first thought to be a non-relevant factor, is in fact quite an important parameter in the CDT at smaller frequency, as we have recently shown.11 Indeed, a phase φ = π/2 produces a much better dynamic localization than any other possible phase φ, and consequently it is our choice here.Since H is periodic in time (H(t) = H(t + τ ), where τ = 2π/ω is the period) we can make use of the standard Floquet theory 7,12 and write the solutions of the time-dependent Schrödinger equation as ψ(t) = exp(−iεt/h)u(t), where u(t), the so-called Floquet state, is also periodic in time with the same period τ , and ε is the Floquet characteristic expone...

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“…We give an explicit analytical representation for electronic states as a function of the intensity and frequency of the electric field. Under the two level approximation, two particular cases are studied: the low-and high-frequency regimes, which result of comparing the ac-field frequency to the characteristic level splitting at zero field.The dynamics of charged particles in semiconductor structures under a time-dependent external electric field has been a topic of intense research [1,2,3,4,5]. The progress of techniques on the nanoscale has made possible the systematic study of effects only present in intense alternating fields in this domain.…”

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confidence: 99%

“…The dynamics of charged particles in semiconductor structures under a time-dependent external electric field has been a topic of intense research [1,2,3,4,5]. The progress of techniques on the nanoscale has made possible the systematic study of effects only present in intense alternating fields in this domain.…”

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confidence: 99%

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AC‐Stark effect in a semi‐spherical quantum dot

Aguilar

Meza-Montes

Trallero‐Giner

et al. 2005

Physica Status Solidi (b)

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We present a theoretical approach to study the effects of an ac-field applied to quantum dots with semi-spherical symmetry. Using the Floquet formalism for this periodically driven system, the timedependent Hamiltonian in the effective mass approximation is solved. We show that the Hilbert space of solutions is separated into orthogonal subspaces with different z-component of the angular momentum. We give an explicit analytical representation for electronic states as a function of the intensity and frequency of the electric field. Under the two level approximation, two particular cases are studied: the low-and high-frequency regimes, which result of comparing the ac-field frequency to the characteristic level splitting at zero field.The dynamics of charged particles in semiconductor structures under a time-dependent external electric field has been a topic of intense research [1,2,3,4,5]. The progress of techniques on the nanoscale has made possible the systematic study of effects only present in intense alternating fields in this domain.In this paper we address the problem of a quantum dot (QD) of semi-spherical shape with the ac-field along the axial symmetry of the dot (z-axis in this case) in a nonperturbative approach. To do so we make use of the Floquet formalism [1]. The Hamiltonian for an electron in the QD under an electric field of intensity F and frequency ω can be written aswhere H o = −(h 2 /2m * )∇ 2 + V o is the Hamiltonian for the nondriven system. Here V o = 0 inside the QD and we use hard-wall boundary conditions, m * is the effective mass of the electron in the QD. In the absence of the ac field the problem is exactly soluble and its eigenenergies are given by the square of the zeroes µ (l) n of the spherical Bessel functions, where n is the order of the zero and l the order of the Bessel function J l+1/2 (see details in [6]). The eigenfunctions, in spherical coordinates, are given bywhere P |m| l are the associated Legendre polinomials, m is the z-component of the angular momentum, and N J and N P are normalization constants.The dynamics of the driven system is governed by the time-dependent Schroedinger equationSince H is periodic in time with period τ = 2π/ω, it is possible to use the standard Floquet theory [1] and write the wavefunction as Ψ = exp(−i ε t/h)Φ, which allows us to rewrite Eq. (3) aswhere ε is a real-valued parameter termed the Floquet characteristic exponent, or the quasienergy. To solve Eq. (4), Φ can be expanded in a Fourier series for the temporal component and linear combinations of stationary states Φ(r, θ, φ, t) = ∞ p=−∞ exp(i p ω t) u p (r, θ, φ), p ∈ Z,

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Nonperturbative electron dynamics in crossed fields

Cited by 21 publications

References 43 publications

Perturbative results on localization for a driven two-level system

Perturbative results on localization for a driven two-level system

Selective coherent destruction of tunneling in a quantum-dot array

AC‐Stark effect in a semi‐spherical quantum dot

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