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Journal of Physics D Applied Physics

Adiabatic passage in quantum wells

Kevin L. Shuford, Jeffrey L. Krause

Published Feb 14, 2003• 2 citations

Abstract

We show that electronic population can be switched adiabatically between the wells of a biased, asymmetric double quantum well (QW) structure. A time-dependent dc field guides an initial state along a smooth path to a state that is localized in a specified QW. General requirements for adiabaticity are determined that manifest the conditions in which the transfer process is optimal. The time duration of the perturbation is a sensitive parameter that influences strongly the outcome of the adiabatic passage. If the perturbation occurs too rapidly, the states mix, and a time-varying superposition state is created. However, if the requirements of adiabaticity are satisfied at all times during the perturbation, the system remains in a pure state, and evolves adiabatically to the final state. Various forms of the dc field are compared, and their relative performance evaluated. The optimal field for efficient adiabatic passage varies from structure to structure, and depends on the response of the system to the dc field. Complex field shapes can be used to produce multiple shifts in electronic density between the QWs. This procedure provides an effective means to perform adiabatic passage in semiconductor heterostructures, with smooth transitions, selectivity, and reversibility.

DOI: 10.1088/0022-3727/36/5/305

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We show that electronic population can be switched adiabatically between the wells of a biased, asymmetric double quantum well (QW) structure. A time-dependent dc field guides an initial state along a smooth path to a state that is localized in a specified QW. General requirements for adiabaticity are determined that manifest the conditions in which the transfer process is optimal. The time duration of the perturbation is a sensitive parameter that influences strongly the outcome of the adiabatic passage. If the perturbation occurs too rapidly, the states mix, and a time-varying superposition state is created. However, if the requirements of adiabaticity are satisfied at all times during the perturbation, the system remains in a pure state, and evolves adiabatically to the final state. Various forms of the dc field are compared, and their relative performance evaluated. The optimal field for efficient adiabatic passage varies from structure to structure, and depends on the response of the system to the dc field. Complex field shapes can be used to produce multiple shifts in electronic density between the QWs. This procedure provides an effective means to perform adiabatic passage in semiconductor heterostructures, with smooth transitions, selectivity, and reversibility.

Adiabatic passage employs a slowly varying time-dependent Hamiltonian to control the evolution of a quantum system along the Hamiltonian eigenstates. For processes of finite duration, the exact time-evolving state may deviate from the adiabatic eigenstate at intermediate times, but in numerous applications it is observed that this deviation reaches a maximum and then decreases significantly towards the end of the process. We provide a straightforward theoretical explanation for this welcome but often unappreciated fact. Our analysis emphasizes a separate adiabaticity criterion for high-fidelity state-to-state transfer and it points to new effective shortcut strategies for near-adiabatic dynamics.

The basic technique of stimulated Raman adiabatic passage for laser-induced adiabatic population transfer between discrete quantum states of an asymmetric double quantum well has been used in our study. The results show that the proper time-delay, overlap, and detuning of two pulses allows the coherent transfer between the states of a double quantum well system, leading to the possibility of implementation of semiconductor–based quantum logic gates and high efficiency optical switches. The impact of phase relaxation on the population transfer efficiency is also studied.

We discuss adiabatic quantum phenomena at a level crossing. Given a path in the parameter space which passes through a degeneracy point, we find a criterion which determines whether the adiabaticity condition can be satisfied. For paths that can be traversed adiabatically we also derive a differential equation which specifies the time dependence of the system parameters, for which transitions between distinct energy levels can be neglected. We also generalize the well-known geometric connections to the case of adiabatic paths containing arbitrarily many level-crossing points and degenerate levels.

Abstract In many quantum technologies adiabatic processes are used for coherent quantum state operations, offering inherent robustness to errors in the control parameters. The main limitation is the long operation time resulting from the requirement of adiabaticity. The superadiabatic method allows for faster operation, by applying counterdiabatic driving that corrects for excitations resulting from the violation of the adiabatic condition. In this article we show how to construct the counterdiabatic Hamiltonian in a system with forbidden transitions by using two-photon processes and how to correct for the resulting time-dependent ac-Stark shifts in order to enable population transfer with unit fidelity. We further demonstrate that superadiabatic stimulated Raman passage can realize a robust unitary NOT-gate between the ground state and the second excited state of a three-level system. The results can be readily applied to a three-level transmon with the ladder energy level structure.

We introduce the ``shaped-adiabatic-passage'' method that allows one to realize a complete population transfer from a given state

|1〉

to superpositions of energy eigenstates $|\ensuremath{\Psi}〉={\ensuremath{\sum}}_{k}{c}_{k}{e}^{\ensuremath{-}i{\ensuremath{\omega}}_{k}t}|k〉$ of any desired composition. This objective can be achieved by using a ``shaped'' (dump or Stokes) laser pulse, formed by simultaneous monochromatic pulses of the same smooth profile, resonantly coupling the states

|k〉

with a single intermediate state

|2〉,

followed by a (pump or anti-Stokes) pulse, coupling this intermediate state with the initial state

|1〉.

The pulse shapes can be obtained from first-order perturbation theory, so the method can be used for efficient information coding in the form of superpositions of atomic Rydberg states or of molecular vibrational states.