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arXiv:1711.08259

Dynamics of quantum collapse in coupled quantum dots

Heber R. da Cruz

Published Nov 22, 2017• 0 citations
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Abstract

In this letter, we have considered an electron in a coupled quantum dot system interacting with a detector represented by a point contact. We present a dynamical model for wave function collapse in the strong coupling to the detector limit. In our model, the electron in the double quantum dot makes a fast transition minimizing the emission of electromagnetic radiation. In this way, a principle of leats emitted radiation can provide a possible description of wave function collapse.

DOI
10.48550/arxiv.1711.08259

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In this letter, we have considered an electron in a coupled quantum dot system interacting with a detector represented by a point contact. We present a dynamical model for wave function collapse in the strong coupling to the detector limit. In our model, the electron in the double quantum dot makes a fast transition minimizing the emission of electromagnetic radiation. In this way, a principle of leats emitted radiation can provide a possible description of wave function collapse.
In this letter, we have considered an electron in a double quantum dot system interacting with a detector represented by a point contact. We present a dynamical model for the gradual decoherence of the density matrix due to the interaction with the detector. The interaction of the qubit (quantum system) on the quantum point contact (environment) leads to a discrete set of pointer states of the double quantum dot (apparatus). The necessary time for the qubit decoherence process (measurement time) has been calculated through this model. The existence of a minimum time for the quantum measurement has been obtained.
Entanglement between a particle and a detector is known to be inherent in the measurement process. Gurvitz recently analyzed the coupling of an electron in a double dot (DD) to a quantum point contact (QPC) detector. In this paper we examine the dynamics of entanglement that result between the DD and QPC. The rate of entanglement is optimized as a function of coupling when the electron is initially in one of the dots. It decreases asymptotically towards zero with increased coupling. The opposite behavior is observed when the DD is initially in a superposition: the rate of entanglement increases unboundedly as the coupling is increased. The possibility that there are conditions for which measurement occurs versus entanglement is considered.
We study the dynamics of two electron spins in coupled quantum dots (CQDs) monitored by a quantum point contact (QPC) detector. Their quantum state can be measured by embedding the QPC in an LC circuit. We derive the Bloch-type rate equations of the reduced density matrix for CQDs. Special attention is paid to the numerical results for the weak measurement condintion under a strong Coulomb interaction. It is shown that the evolution of QPC current always follows that of electron occupation in the right dot. In addition, we find that the output voltage of the circuit can reflect the evolution of QPC current when the circuit and QPC are approximately equal in frequency. In particular, the wave shape of the output voltage can be improved by adjusting the circuit resonance frequency and bandwidth.
We consider the model of quantum dots interacting with coherent radiation when the relaxation processes may be neglected. The system under investigation consists of two discrete energy levels of the quantum dots in the presence of strong electron-electron Coulomb interaction and the transitions between these levels in response to electromagnetic radiation. By using the suitable generalisation of the Hubbard model the system of equations describing the evolution of the state of quantum dot was derived.
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In this work, we have studied the post-measurement dynamics of several electrons in a double quantum dot system using a new method of calculation. We have solved the effective-mass non-linear Schrödinger equation for two electron wave packets in a double quantum well taking into account the different number of projected electrons in each quantum well after an observation. It is found the existence of a critical density that reduces strongly the tunneling dynamics between both quantum wells. In addition, we have shown the possibility of having a new kind of electromagnetic radiation emerging from a semiconductor device after a quantum observation.