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Saturation nonlinearities of cavity-QED enhanced optical circular birefringence in microcavities containing a charged quantum dot

C. Y. Hu, John G. Rarity

Published Sep 12, 2014• 0 citations
OpenAlex

Abstract

Giant optical Faraday rotation (GFR) and giant optical circular birefringence (GCB) induced by a single quantum-dot spin in an optical microcavity can be regarded as linear effects in the weak-excitation approximation if the input field lies in the low-power limit [Hu et al, Phys.Rev. B {\bf 78}, 085307(2008) and ibid {\bf 80}, 205326(2009)]. In this work, we investigate the transition from the weak-excitation approximation moving into the saturation regime comparing a semiclassical approximation with the numerical results from a quantum optics toolbox [S.M. Tan, J. Opt. B {\bf 1}, 424 (1999)]. We find that the GFR and GCB around the cavity resonance in the strong coupling regime are input-field independent at intermediate powers and can be well described by the semiclassical approximation. Those associated with the dressed state resonances in the strong coupling regime or merging with the cavity resonance in the Purcell regime are sensitive to input field at intermediate powers, and cannot be well described by the semiclassical approximation due to the quantum dot saturation. As the GFR and GCB around the cavity resonance are relatively immune to the saturation effects, the rapid read out of single electron spins can be carried out with coherent state and other statistically fluctuating light fields. This also shows that high speed quantum entangling gates, robust against input power variations, can be built exploiting these linear effects.

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Giant optical Faraday rotation (GFR) and giant optical circular birefringence (GCB) induced by a single quantum-dot spin in an optical microcavity can be regarded as linear effects in the weak-excitation approximation if the input field lies in the low-power limit [Hu et al, Phys.Rev. B {\bf 78}, 085307(2008) and ibid {\bf 80}, 205326(2009)]. In this work, we investigate the transition from the weak-excitation approximation moving into the saturation regime comparing a semiclassical approximation with the numerical results from a quantum optics toolbox [S.M. Tan, J. Opt. B {\bf 1}, 424 (1999)]. We find that the GFR and GCB around the cavity resonance in the strong coupling regime are input-field independent at intermediate powers and can be well described by the semiclassical approximation. Those associated with the dressed state resonances in the strong coupling regime or merging with the cavity resonance in the Purcell regime are sensitive to input field at intermediate powers, and cannot be well described by the semiclassical approximation due to the quantum dot saturation. As the GFR and GCB around the cavity resonance are relatively immune to the saturation effects, the rapid read out of single electron spins can be carried out with coherent state and other statistically fluctuating light fields. This also shows that high speed quantum entangling gates, robust against input power variations, can be built exploiting these linear effects.
Giant optical Faraday rotation (GFR) and giant optical circular birefringence (GCB) induced by a single quantum-dot spin in an optical microcavity can be regarded as linear effects in the weak-excitation approximation if the input field lies in the low-power limit [Hu et al., Phys. Rev. B 78, 085307 (2008); Hu et al., Phys. Rev. B 80, 205326 (2009)]. In this work, we investigate the transition from the weak-excitation approximation moving into the saturation regime comparing a semiclassical approximation with the numerical results from a quantum optics toolbox [Tan, J. Opt. B 1, 424 (1999)]. We find that the GFR and GCB around the cavity resonance in the strong-coupling regime are input field independent at intermediate powers and can be well described by the semiclassical approximation. Those associated with the dressed state resonances in the strong-coupling regime or merging with the cavity resonance in the Purcell regime are sensitive to input field at intermediate powers, and cannot be well described by the semiclassical approximation due to the quantum-dot saturation. As the GFR and GCB around the cavity resonance are relatively immune to the saturation effects, the rapid readout of single-electron spins can be carried out with coherent state and other statistically fluctuating light fields. This also shows that high-speed quantum entangling gates, robust against input power variations, can be built exploiting these linear effects.
Giant optical circular birefringence (GCB) induced by a single quantum-dot-confined spin in an optical microcavity finds wide applications in quantum and optical technologies, such as quantum gates, quantum transistors, quantum repeaters, quantum routers, etc. If the system is probed with a classical light, such as the laser light where the photons are uncorrelated with each other, then the single-photon GCB is detected. In this work we develop a general approach to investigate the many-body dynamics of nnn photons bound to one quantum emitter and apply this method to calculate the nnn-photon GCB probed with quantum light in Fock states. With suppressed atomic saturation, quantum light loads photons into dressed states more efficiently than classical light such that the whole Jaynes-Cummings energy ladder and the quantum nonlinearity related to the multiphoton transitions can be observed. The nnn-photon GCB lying at the cavity mode resonance allows the spin-cavity quantum gates and quantum transistors to extend from single-photon to nnn-photon operations and generate entangled photonic Fock states, i.e., the NOON states which are useful for quantum metrology and lithography.
We propose a quantum nondemolition method---a giant optical Faraday rotation near the resonant regime to measure a single-electron spin in a quantum dot inside a microcavity where a negatively charged exciton strongly couples to the cavity mode. Left-circularly and right-circularly polarized lights reflected from the cavity obtain different phase shifts due to cavity quantum electrodynamics and the optical spin selection rule. This yields giant and tunable Faraday rotation that can be easily detected experimentally. Based on this spin-detection technique, a deterministic photon-spin entangling gate and a scalable scheme to create remote spin entanglement via a single photon are proposed.
A two-level system that is coupled to a high-finesse cavity in the Purcell regime exhibits a giant optical nonlinearity due to the saturation of the two-level system at very low intensities, of the order of one photon per lifetime. We perform a detailed analysis of this effect, taking into account the most important practical imperfections. Our conclusion is that an experimental demonstration of the giant nonlinearity is feasible using semiconductor micropillar cavities containing a single quantum dot in resonance with the cavity mode.
Achieving strong optical nonlinearity in a low excitation power level is crucial in micro- and nanophotonics, central to many applications. Here, we explore optical linear and nonlinear responses in a single quantum dot (QD) embedded into a single-mode cavity under the effect of an external magnetic field and a continuous-wave laser excitation in the weak-coupling regime. Using experimentally realistic parameters, we find that the magnetic field introduced in such a coupled cavity-QD system can drastically modify the properties of photons and thus can be employed as a flexible control parameter. Especially, the enhanced optical Kerr nonlinearity can be achieved by tuning the applied magnetic field appropriately, which can reach over 11-fold improvement as compared to the case without the magnetic field. Physically, this is the consequence of the magnetic-field-induced resonance shifts and the cavity-field-mediated interferences. As an example of its applications, in the basis of this attainable strong Kerr nonlinearity, we show a feasible way of generating an optical high-order sideband efficiently, with small sideband spacing, as small as a few tens of megahertz, and low input excitation power, as low as a few nanowatts. Moreover, the manipulation of the high-order sideband is also discussed by changing the magnetic field from 0 to 3 T, where the variation of the sideband power is in good agreement with that of the Kerr nonlinearity. Considering realistic experimental conditions we elaborate the possible implementation of our proposal. In addition to being of fundamental interest, the results of our paper hold potential in optical frequency combs, nonlinear optics, and high precision measurement.
We investigate the possibility of achieving scalable photonic quantum computing by the giant optical circular birefringence induced by a quantum-dot spin in a double-sided optical microcavity as a result of cavity quantum electrodynamics. We construct a deterministic controlled-not gate on two photonic qubits by two single-photon input-output processes and the readout on an electron-medium spin confined in an optical resonant microcavity. This idea could be applied to multi-qubit gates on photonic qubits and we give the quantum circuit for a three-photon Toffoli gate. High fidelities and high efficiencies could be achieved when the side leakage to the cavity loss rate is low. It is worth pointing out that our devices work in both the strong and the weak coupling regimes.