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arXiv:0801.1871 · Journal of Nanophotonics

Theoretical aspects of quantum state transfer, correlation measurement and electron-nuclei coupled dynamics in quantum dots

T. Takagahara, Özgür Çakır

Published Dec 1, 2007• 3 citations
arXivHTMLPDF

Abstract

Photons and electrons are the key quantum media for the quantum information processing based on solid state devices. The essential ingredients to accomplish the quantum repeater were investigated and their underlying physics were revealed. The relevant elementary processes of the quantum state transfer between a single photon and a single electron were analyzed, to clarify the conditions to be satisfied to achieve the high fidelity of the quantum state transfer. An optical method based on the Faraday rotation was proposed to carry out the Bell measurement of two electrons which is a key operation in the entanglement swapping for the quantum repeater and its feasibility was confirmed. Also investigated was the quantum dynamics in the electron-nuclei coupled spin system in quantum dots and a couple of new phenomena were predicted related to the correlations induced by the hyperfine interaction, namely, bunching and revival in the electron spin measurements. These findings will pave the way to accomplish the efficient and robust quantum repeater and nuclear spin quantum memory.

DOI
10.1117/1.2828099

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•Dec 21, 2016•0 citations
Photons and electrons are the key quantum media for the quantum information processing based on solid state devices. The essential ingredients to accomplish the quantum repeater were investigated and their underlying physics were revealed. The relevant elementary processes of the quantum state transfer between a single photon and a single electron were analyzed, to clarify the conditions to be satisfied to achieve the high fidelity of the quantum state transfer. An optical method based on the Faraday rotation was proposed to carry out the Bell measurement of two electrons which is a key operation in the entanglement swapping for the quantum repeater and its feasibility was confirmed. Also investigated was the quantum dynamics in the electron-nuclei coupled spin system in quantum dots and a couple of new phenomena were predicted related to the correlations induced by the hyperfine interaction, namely, bunching and revival in the electron spin measurements. These findings will pave the way to accomplish the efficient and robust quantum repeater and nuclear spin quantum memory.
We investigate quantum dynamics in the electron-nuclei coupled spin system in quantum dots and clarify the fundamental features of quantum correlation induced via successive electron-spin measurements. This quantum correlation leads to interesting phenomena such as the bunching of outcomes in the electron-spin measurements and the revival of an arbitrary initial electron-spin state. The nuclear spin system is also affected by the quantum correlation and is, in fact, squeezed via conditional measurements or postselection. This squeezing is confirmed by calculating the increase in the purity of the nuclear spin system. Thus, the successive electron-spin measurements provide a probabilistic method to squeeze the nuclear spin system. These new features are predicted not only for the case of double quantum dots occupied by a pair of electrons but also for the case of a single quantum dot occupied by a single electron or a pair of electrons.
We have investigated the quantum dynamics of the electron-nuclei coupled system in a double quantum dot and discovered a couple of new phenomena related to the quantum nature of nuclear spin system. Especially, the bunching of results of the electron spin measurements and the revival in the conditional probabilities are salient features of quantum dynamics. The underlying mechanism is the squeezing of the nuclear spin state through the electron spin measurements. This squeezing is expected to lead to the elongation of the electron spin coherence time. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Recently, a quantum media converter from a photon qubit to an electron spin qubit was proposed for quantum repeaters. Quantum information can take several different forms and it is preferable to be able to convert among different forms. One form is the photon polarization and another is the electron spin polarization. Photons are the most convenient medium for sharing quantum information between distant locations. However, it is necessary to realize a quantum repeater in order to send the information securely over a very long distance overcoming the photon loss. A quantum repeater requires quantum information storage and the electron spin is a promising candidate of such a quantum memory because of its long decoherence time. The most important ingredient of the quantum repeater is the entanglement swapping through the Bell (correlation) measurement. We propose an optical means to carry out the correlation measurement. The advantage of this method is the nondestructive character which keeps the quantum state unchanged.
The decoherence of entanglement states stored in quantum memory is a major obstacle when implementing a quantum repeater. So far, the electron spins in quantum dots are usually utilized to construct entangled states in quantum repeater. In the quantum repeater process, the distance between quantum dots is large, so the interaction between them can be neglected. Thus the hyperfine interaction between the electron spin and its neighbor nuclear spins in the quantum dot is considered to be the main reason for the decoherence of the system. In early researches, the hyperfine interaction between the electron spin and its neighbor nuclear spins was considered as an effective magnetic field whose magnitude and direction are random and the magnitude follows the Gaussian distribution. In this paper, we simultaneously consider an applied magnetic field and the interaction between the electron spin and its neighbor nuclear spins, and investigate the decoherence of the quantum repeater of two quantum dots. We first solve the time evolution of the system by the numerical method, and the result shows that when the applied magnetic field is increased to a certain value, the four Bell states can be divided into two kinds, each with two Bell states. The system cannot transit from the Bell state in one kind to that in the other kind, but can transit between two Bell states with in the same kind. This effectively improves the fidelity of the initial state and suppresses the decoherence of the system. For a given applied magnetic field with large magnitude, we theoretically study the effect of the fluctuation of nuclear spin on the entangled state, and give an analytical expression for each of the fidelity and the decoherence time of the initial state. We show that the decoherence times of the four Bell states are the same, but the time evolutions of the Bell states belonging to different kinds are different obviously. The fidelity of two Bell states not only decays exponentially but also oscillates rapidly, so such two Bell states are difficult to be manipulated and not suggested in quantum repeater process. The results in this paper are expected to provide theoretical suggestions for selecting the entangled states in quantum repeater.
Inspired by recent developments in the control and manipulation of quantum dot nuclear spins, which allow for the transfer of an electron spin state to the surrounding nuclear-spin ensemble for storage, we propose a quantum repeater scheme that combines individual quantum dot electron spins and nuclear-spin ensembles, which serve as spin-photon interfaces and quantum memories respectively. We consider the use of low-strain quantum dots embedded in high-cooperativity optical microcavities. Quantum dot nuclear-spin ensembles allow for the long-term storage of entangled states, and heralded entanglement swapping is performed using cavity-assisted gates. We highlight the advances in quantum dot technologies required to realize our quantum repeater scheme which promises the establishment of high-fidelity entanglement over long distances with a distribution rate exceeding that of the direct transmission of photons.
Self-assembled quantum dots can act as an interface between single spins and photons. They combine the flexibility and scalability of semiconductor systems with near-perfect two level systems, emitting highly coherent single photons. In potential quantum information processing architectures based upon optical networks, quantum dots permit light-matter coupling between matter qubits and photonic links. Single trapped charge carriers in quantum dots can be addressed optically, generating spin-photon entanglement between the matter qubits and \lq flying' photon qubits, a key first step in creation of a network. Such an optically linked network of spins in quantum dots has yet to be realized. The semiconductor environment presents a key challenge; it broadens the spectrum of the emitted light, which reduces the fidelity of schemes based upon photon exchange or interference. In addition, these quantum dots are subject to hyperfine coupling to a bath of >>> 105^{5}5 nuclear spins. While this presents an opportunity to study the physics of a central spin in a spin bath, it degrades the spin coherence of a trapped electron or hole. The suggested gate operations to generate entanglement, and the spin measurements to verify a created state, rely upon photon detection. Thus a second limitation occurs due to low efficiency of detectors and photon collection probability. Recent developments in detector technology have enabled us to bring generation and verification of entangled states with quantum dots into the realm of possibility. This dissertation begins with a detailed study of the interaction of a single electron spin with the solid state environment of the quantum dot, analysing the intensity noise of scattered light under resonant excitation to uncover the timescales and relative amplitudes of identified noise sources. A technique for rapid characterization of samples is presented, focusing in particular upon comparison of spectral broadening of the optical transitions relevant to a spin-photon interface. Having identified the extent of environmental factors acting upon the quantum dots, we turn to a demonstration of photon-mediated entanglement between two distant electron spins using a probabilistic scheme. We are able to generate entangled states at 7 kHz, the fastest yet reported for photon-mediated protocols. The average state fidelity of the created Bell states is 63.5 ±\pm± 3.0 \%., violating the classical limit by over 4 standard deviations of the mean. In addition, we demonstrate full optical phase tuning of the Bell state ∣Ψ=12(∣↑∣↓+eiϕ∣↓∣↑)|{\Psi} = \frac{1}{\sqrt{2}}\left(|{\uparrow}|{\downarrow} + e^{i\phi}|{\downarrow}|{\uparrow} \right)∣Ψ=2​1​(∣↑∣↓+eiϕ∣↓∣↑). This is a proof of principle experiment, and sets a fidelity benchmark upon which gains can be made by mitigation of environmental dynamics.