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arXiv:2008.06442 · Physical review. B./Physical review. B

Quantum Zeno effect and quantum nondemolition spin measurement in a quantum dot–micropillar cavity in the strong coupling regime

N. V. Leppenen, L. Lanco, Dmitry S. Smirnov

Published Jan 14, 2021• 15 citations
arXivHTMLPDF

Abstract

We theoretically describe the quantum Zeno effect in a spin-photon interface represented by a charged quantum dot in a micropillar cavity in the strong coupling regime. This simplest model allows for various generalizations for the different systems. We derive a simple expression for the spin measurement rate, which allows one to tune the electron spin precession frequency in an external magnetic field and spin relaxation time. We calculate the spin noise bispectrum, which reveals the qualitative change of the spin dynamics with an increase of the measurement strength and proves the quantum nature of the spin noise. We also calculate the quantum information gain rate and find the conditions when it equals the spin dephasing rate, i.e., reaches the quantum limit.

DOI
10.1103/physrevb.103.045413

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We theoretically describe the quantum Zeno effect in a spin-photon interface represented by a charged quantum dot in a micropillar cavity in the strong coupling regime. This simplest model allows for various generalizations for the different systems. We derive a simple expression for the spin measurement rate, which allows one to tune the electron spin precession frequency in an external magnetic field and spin relaxation time. We calculate the spin noise bispectrum, which reveals the qualitative change of the spin dynamics with an increase of the measurement strength and proves the quantum nature of the spin noise. We also calculate the quantum information gain rate and find the conditions when it equals the spin dephasing rate, i.e., reaches the quantum limit.
Measurement of the tunneling current of spin-polarized electrons via a molecule with a localized spin provides information on the orientation of that spin. We show that a strong tunneling current due to the shot noise suppresses the spin dynamics, such as the spin precession in an external magnetic field, and the relaxation due to the environment (quantum Zeno effect). A weak tunneling current preserves the spin precession with the oscillatory component of the current of the same order as the noise. We propose an experiment to observe the Zeno effect in a tunneling system and describe how the tunneling current may be used to read a qubit represented by a single spin 1/2.
Measurements performed on a system will alter the dynamics of that system, and in the strong-measurement limit, can theoretically freeze the free evolution completely. This is the quantum Zeno effect. We utilize quantum-nondemolition photon-counting techniques to realize the Zeno effect on the evolution of either a two-level Jaynes-Cummings atom interacting with a resonant cavity mode, or on two electromagnetic modes configured as a multilevel parametric frequency converter. These systems interact with another electromagnetic cavity mode via a quadratic coupling system based on four-wave mixing and constructed so as to be a nondemolition measurement of the photon number. This mode is then coupled to the environment through the cavity mirrors. This measurement is shown to be a measurement of system populations, which generates the desired Zeno effect and in the strong-measurement limit will freeze the free dynamics of the system.
Graph states of mutually entangled photons are key resources for quantum computation and communication and can be generated by leveraging the entanglement between a single resident spin and emitted photons from a charged semiconductor quantum dot (QD). This approach is intrinsically limited by the decoherence of the spin. We study how to mitigate this decoherence with dynamical decoupling of an electron spin in the weak transverse magnetic field regime using spin echo and Carr-Purcell-Meiboom-Gill (CPMG) techniques. Application of these techniques allows us to extend the coherence time of a spin by more than two orders of magnitude, extracting a T2CPMGT_2^{CPMG}T2CPMG​ of 298±53298\pm53298±53 ns. We further demonstrate that this technique is compatible with the generation of a spin-photon-photon entangled state at a high rate enabled by a micropillar cavity, with a 20% improvement in simulated state fidelity when using dynamical decoupling. These results pave the way for generating larger and more complex entangled states with QDs.
Solid state based quantum information processing is focused on physical implementation of all necessary elements of quantum computation and quantum information in solid state systems, mainly due to their scalability compared to e.g. optical systems. Among many proposals to realize these types of devices, such as quantum dots as charge qubits or Josephson junction circuits, we study here one of the most promising candidates, i.e., the spin of an electron confined to a quantum dot as a qubit. Experimentally, it has been shown that the relaxation rate of this two level system can be pushed above few seconds in low magnetic fields. Moreover, using spin echo techniques, \nthe spin dephasing time can be maximized up to milliseconds with the current technology. This long spin decay time is one of the main reasons that make this system desirable for quantum computation and quantum information purposes. \nWe reexamined the recent measurement based proposal called one-way quantum computation which exploits entanglement and local measurements as tools to perform quantum computation on N qubits. Although it was suggested in the original work to entangle the qubits via the nearest neighbor Ising interaction, we investigated how one can generate the so-called cluster states with the Heisenberg interaction. We extended our method to include more general forms of Heisenberg interaction such as asymmetric coupling of adjacent qubits. These forms of couplings, rather than Ising interaction, are more encountered in solid state devices, and therefore make it possible to perform one-way quantum computation with electron spins in quantum dots coupled via exchange interaction to their adjacent spins. \n \nChapters II, III, and IV of my thesis are devoted to the study of the spin-orbit interaction in heterostructure quantum dots and its effect on the spin dynamics. We observed that one can actually use spin-orbit interaction to manipulate the spin state of an electron on time scales much smaller than the spin dephasing time. Specifically, in chapter II, we studied the effect of a nearby functioning quantum point contact (QPC) on the relaxation of the electron spin and show that the charge fluctuations in QPC lead to spin relaxation of the confined electron in the presence of spin-orbit interactiom and an applied magnetic field. We also addressed the relation of this rate to the microscopic parameters of the system and found some geometrical dependence of the spin relaxation time on the orientation of the QPC on the substrate. Moreover, we showed in chapters III and IV that the spin-orbit interaction can play a positive role, in order to rotate the spin around the Bloch sphere. We considered different mechanisms, particularly, Electron Dipole Spin Resonance (EDSR) and holonomic unitary gates in quantum dots. We verified that these mechanisms of spin manipulation can be realized in solid state systems with the state of the art semiconductor technologies. \n \nChapter V of the thesis covers a slightly different topic and focuses on the role of the Coulomb interaction in electronic transport. There, we reviewed the non-analytic corrections to the Fermi liquid behavior and their consequences on the momentum occupation number of the electrons in a two dimensional electron gas (2DEG). As an example, we calculated the tunneling rate from an interacting electron reservoir onto a quantum dot and compared our result to the corresponding case for electron tunneling between bilayer 2DEGs. Moreover, within RPA approximation, we found that the electron-plasmon coupling leads to a quadratic frequency dependence of the electron self-energy at low frequencies at the Fermi surface. This correction suppresses the same order corrections due to the particle-hole bubble. \n \n \n
Continuously monitoring a quantum system can strongly affect its properties and even suppress its coherent evolution via the Quantum Zeno effect. Here we focus on one of the simplest entangled many-body state, arising via the Kondo effect in a strongly interacting quantum dot coupled to a metallic bath, and investigate the effect of continuous monitoring of the dot total charge. We show that the decay rate of an initially polarized spin displays a crossover from Kondo screening to Quantum Zeno effect. Remarkably, the long-lived Kondo state is robust to weak dissipation, as confirmed by the dot spectral function which features a clear Kondo peak at finite dissipation, even in a regime where charge fluctuations and the associated Hubbard bands have been quenched by the monitoring protocol. We derive an effective model for the long-time dynamics which is described, at weak dissipation, by a non-Hermitian Kondo model. The continuous monitoring of entangled many-body states can strongly affect their properties. Here, the authors theoretically show a crossover from Kondo to Zeno screening for an interacting quantum dot coupled to a metallic bath with dissipation.
We describe theoretically the effects of the quantum back action under the continuous optical measurement of electron spins in quantum dots. We consider the system excitation by elliptically polarized light close to the trion resonance, which allows for simultaneous spin orientation and measurement. We microscopically demonstrate that the nuclei-induced spin relaxation can be both suppressed and accelerated by the continuous spin measurement due to the quantum Zeno and anti-Zeno effects, respectively. Our theoretical predictions can be directly compared with the future experimental results and straightforwardly generalized for pump-probe experiments.