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arXiv:1610.06482 · Physical review. B./Physical review. B

Generation of Schrödinger cat type states in a planar semiconductor heterostructure

Jarosław Pawłowski, M. Górski, G. Skowron, S. Bednarek

Published Sep 18, 2017• 11 citations
arXivHTMLPDF

Abstract

We propose a nanodevice based on a typical planar semiconductor heterostructure with lateral confinement potential created by voltages applied to local gates. We show how to obtain near parabolical confinement along the nanodevice, and how to use coherent states of the harmonic oscillator for spatial separation of electron densities corresponding to opposite spin directions. In such a way, an entangled state of Schr\"odinger's cat type is created. We have performed simulations of a realistic nanodevice model by numerically solving the time-dependent Schr\"odinger equation together with simultaneous tracking of the controllable confinement potential via solution of the Poisson's equation at every time step.

DOI
10.1103/physrevb.96.115308

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A nanodevice capable of separating spins of two electrons confined in a quantum dot formed in a gated semiconductor nanowire is proposed. Two electrons confined initially in a single quantum dot in the singlet state are transformed into the system of two electrons confined in two spatially separated quantum dots with opposite spins. In order to separate the electrons' spins we exploit transitions between the singlet and the triplet state, which are induced by resonantly oscillating Rashba spin-orbit coupling strength. The proposed device is all electrically controlled and the electron spin separation can be realized within tens of picoseconds. The results are supported by solving numerically the quasi-one-dimensional time-dependent Schroedinger equation for two electrons, where the electron-electron correlations are taken into account in the exact manner.
Mesoscopic quantum superpositions, or Schrödinger cat states, are widely studied for fundamental investigations of quantum measurement and decoherence as well as applications in sensing and quantum information science. The generation and maintenance of such states relies upon a balance between efficient external coherent control of the system and sufficient isolation from the environment. Here we create a variety of cat states of a single trapped atom's motion in a harmonic oscillator using ultrafast laser pulses. These pulses produce high fidelity impulsive forces that separate the atom into widely separated positions, without restrictions that typically limit the speed of the interaction or the size and complexity of the resulting motional superposition. This allows us to quickly generate and measure cat states larger than previously achieved in a harmonic oscillator, and create complex multi-component superposition states in atoms.Generation of mesoscopic quantum superpositions requires both reliable coherent control and isolation from the environment. Here, the authors succeed in creating a variety of cat states of a single trapped atom, mapping spin superpositions into spatial superpositions using ultrafast laser pulses.
We investigate numerically the charge, spin, and entanglement dynamics of two electrons confined in a gated semiconductor nanowire. The electrostatic coupling between electrons in the nanowire and the induced charge on the metal electrodes leads to a self-trapping of the electrons, which results in solitonlike properties. We show that the interplay of an all-electrically controlled coherent transport of the electron solitons and of the exchange interaction can be used to realize ultrafast SWAP and entangling SWAP\sqrt{\text{SWAP}}SWAP​ gates for distant spin qubits. We demonstrate that the latter gate can be used to generate a maximally entangled spin state of spatially separated electrons. The results are obtained by quantum-mechanical time-dependent calculations with exact inclusion of electron-electron correlations.
We present theory and calculations for coherent high-fidelity quantum control of many-particle states in semiconductor quantum wells. We show that coupling a two-electron double quantum dot to a terahertz optical source enables targeted excitations that are one to two orders of magnitude faster and significantly more accurate than those obtained with electric gates. The optical fields subject to physical constraints are obtained through quantum optimal control theory that we apply in conjunction with the numerically exact solution of the time-dependent Schr\"odinger equation. Our ability to coherently control arbitrary two-electron states, and to maximize the entanglement, opens up further perspectives in solid-state quantum information.
The quantum properties of superradiant pulses generated at the radiative recombination of an electron–hole condensate in semiconductor heterostructures at room temperature have been studied using optical homodyne tomography. Signatures of the quantum entanglement of superradiant states, which are superpositions of two coherent states, have been revealed. It has been demonstrated that reconstructed Wigner functions under certain conditions are very similar to the Wigner functions of the Schrödinger cat states.
A solid-state implementation of a universal set of gates for quantum computation is proposed and analysed using a time-dependent 2D Schrödinger solver. The qubit is defined as the state of an electron propagating along a couple of quantum wires. The wires are suitably coupled through a potential barrier with variable height and/or width. It is shown how a proper design of the system allows the implementation of any one-qubit transformation. The two-qubit gate is realized through a Coulomb coupler able to entangle the quantum states of two electrons running in two wires of two different qubits. The simulated devices are GaAs—AlGaAs heterostructures that should be on the borderline of present semiconductor technology. An estimate of decoherence effects due to phonon scattering is also presented.