Two-level systems: Exact solutions and underlying pseudo-supersymmetry

Shamshutdinova, V. V.; Samsonov, B. F.; Гитман, Д. М.

doi:10.1016/j.aop.2006.05.004

Cited by 7 publications

(7 citation statements)

References 40 publications

(90 reference statements)

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“…The properties of such chains were analyzed in detail in [26]. The results obtained in the present work allow a large family of new exactly solvable biases to be constructed for equation (1).…”

Section: Exactly Solvable Bias Pulsesmentioning

confidence: 94%

“…Starting from the simplest case 0 const ε = ε = , a family of new nontrivial potentials (biases), for which Schrödinger's equation (1) could be solved exactly, was found. In the present work, we take advantage of the results obtained in [24][25][26][27] to describe the time evolution of the flux qubit and the time dependence of the qubit localization probability and to calculate its time-averaged values. Let us consider first the behavior of the flux qubit with the bias ( )…”

Section: Exactly Solvable Bias Pulsesmentioning

confidence: 99%

“…Then the states } { 0 , 1 of the flux qubit have the definite (clockwise or counterclockwise) direction of superconducting current circulating in the loop. The above-mentioned non-periodic time-dependent bias pulses are the potentials for which Schrödinger's equation (1) can be solved exactly [24][25][26][27]. Thus, the probability calculated using these exact solutions is, for example, the probability P ↑ of the clockwise current direction.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamics of superconducting qubits with exactly solvable bias pulses

Shamshutdinova

Kiyko²,

Shevchenko³

et al. 2008

Russ Phys J

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The dynamics of a quantum two-state system (qubit) with external control bias pulses of special shapes is considered. The bias pulses represent the potentials for which the Schrödinger equation can be solved exactly. The probability to register a definite direction of the current in a loop and its time-averaged values are calculated for the flux qubit; calculations are performed both analytically and numerically in the presence of relaxation and decoherence within the framework of the density matrix formalism. It is demonstrated that there exist external bias pulses for which the definite current direction probability is a monotonically increasing function of time that approaches a limiting value exceeding 1/2. The probability to find the system in the excited state is calculated, and the possibility of inverse population in a properly driven two-state system is demonstrated given that the relaxation and decoherence rates are small enough.

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Section: Exactly Solvable Bias Pulsesmentioning

confidence: 94%

Section: Exactly Solvable Bias Pulsesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics of superconducting qubits with exactly solvable bias pulses

Shamshutdinova

Kiyko²,

Shevchenko³

et al. 2008

Russ Phys J

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“…3. By combining the ϕ, θ, α functions of the two above examples it is possible to construct 6 fields more in the form (9) that are restricted in time, with the exact solutions given by (5).…”

Section: Exact Solutions For Some Restricted In Time External Fieldsmentioning

confidence: 99%

“…The best known physical system that could be identified with a two-level system is a fixed spin-one-half object interacting with a magnetic field. The two-level system have been studied by many authors using different methods, see for example [4,5]. Likewise the fourlevel systems can be used to describe two interacting one-half spins, e.g., the valence electrons in two coupled semiconductor quantum dots [6].…”

Section: Introductionmentioning

confidence: 99%

Two- and Four-Level Systems in Magnetic Fields Restricted in Time

et al. 2011

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We describe some new exact solutions for two-and four-level systems. In all the cases, external fields have a restricted behavior in time. First, we consider a method to construct new solutions for onespin equation and give some explicit examples: One of them is in a external magnetic field that acts during a finite time interval. Then we show how these solutions can be used to solve the two-spin equation problem. A solution for two interacting spins is analyzed in the case when the field difference between the external fields in each spin varies adiabatically, vanishing on the time infinity. The latter system can be identified with a quantum gate realized by two coupled quantum dots. The probability of the Swap operation for such a gate can be explicitly expressed in terms of special functions. Using the obtained expressions, we construct plots for the Swap operation for some parameters of the external magnetic field and interaction function.

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Non-Markovian entanglement dynamics of two qubits interacting with a common electromagnetic field

Anastopoulos

Shresta

Hu³

2009

Quantum Inf Process

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We study the non-equilibrium dynamics of a pair of qubits made of two-level atoms separated in space with distance r and interacting with one common electromagnetic field but not directly with each other. Our calculation makes a weak coupling assumption but no Born or Markov approximation. We write the evolution equations of the reduced density matrix of the two-qubit system after integrating out the electromagnetic field modes. We study two classes of states in detail: Class A is a one parameter family of states which are the superposition of the highest energy and lowest energy states, and Class B states which are the linear combinations of the symmetric and the antisymmetric Bell states. Our results for an initial Bell state are similar to those obtained before for the same model derived under the Born-Markov approximation. However, in the Class A states the behavior is qualitatively different: under the non-Markovian evolution we do not see sudden death of quantum entanglement and subsequent revivals, except when the qubits are sufficiently far apart.We provide explanations for such differences of behavior both between these two classes of states and between the predictions from the Markov and non-Markovian dynamics. We also study the decoherence of this two-qubit system.

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Two-level systems: Exact solutions and underlying pseudo-supersymmetry

Cited by 7 publications

References 40 publications

Dynamics of superconducting qubits with exactly solvable bias pulses

Dynamics of superconducting qubits with exactly solvable bias pulses

Two- and Four-Level Systems in Magnetic Fields Restricted in Time

Non-Markovian entanglement dynamics of two qubits interacting with a common electromagnetic field

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