Quantum feedback of a double-dot qubit

We discuss an experimental proposal on quantum feedback control of a double-dot qubit, which seems to be within the reach of the present-day technology. Similar to the earlier proposal, the feedback loop is used to maintain the coherent oscillations in the qubit for an arbitrary long time; however, this is done in a significantly simpler way. The main idea is to use the quadrature components of the noisy detector current to monitor approximately the phase of qubit oscillations. q 2005 Elsevier Ltd. All rights reserved. The principle of feedback control is widely used in physics and engineering. However, continuous feedback control of quantum systems is a relatively new and not well studied subject. Quantum feedback in optics has been proposed theoretically a decade ago [1] and has been recently demonstrated experimentally [2]. For a solid-state system (qubit), the quantum feedback has been discussed for the first time only few years ago [3], and there are no experiments yet. The possibility of a quantum feedback is based on the fact that measurement by an ideal solid-state detector (with 100% quantum efficiency h) does not decohere a single qubit [4,5], even though it decoheres an ensemble of qubits because each qubit evolves in a different way. An example of theoretically ideal detector is [4] the quantum point contact (h comparable to 1 has been demonstrated experimentally [6]). The random evolution of a qubit in the process of measurement can be monitored using the noisy detector output [4,5], and this monitoring can naturally be used for continuous feedback control of the qubit. In the proposal of Ref. [3], the quantum feedback is used to maintain quantum coherent (Rabi) oscillations in a qubit for an arbitrary long time, synchronizing them with an external classical signal. This is done by measuring the noisy current I(t) in a weakly coupled detector and using the quantum Bayesian equations [4] to translate information contained in I(t) into 0026-2692/$ see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2005.02.019 * Tel.: C1 951827 2345; fax: C1 951 827 2425. E-mail address: [email protected]. the evolution of qubit density matrix r(t). After that r(t) is compared with the desired quantum state rd(t), and the calculated difference is used to control the qubit Hamiltonian in order to decrease the difference. An important difficulty in such experiment is a necessity to solve the Bayesian equations in real time. Moreover, the bandwidth of the line delivering I(t) to the circuit solving the Bayesian equations, should be significantly wider than the Rabi frequency U. Unfortunately, these conditions are unrealistic for the present-day experiments with solid-state qubits. In this paper, we discuss (see also Ref. [7]) a much simpler way (Fig. 1) of processing the information carried by the detector current I(t). The idea is to use the fact that besides noise, I(t) contains an oscillating contribution due to Rabi oscillations in the measured qubit. Therefore, if we apply I(t) to a simple tank circuit (which is in resonance with U), then the phase of the tank circuit oscillations will depend on the phase of Rabi oscillations. Instead of using the tank circuit, almost equivalent theoretically procedure is to mix I(t) with the signal from a local oscillator (Fig. 1) in order to determine two quadrature amplitudes of I(t) at frequency U, which will carry information on the phase of Rabi oscillations. Since diffusion of the Rabi phase is a slow process (assuming weak coupling to the detector and environment), the further circuitry can be relatively slow, limited by the qubit dephasing rate, but not limited by much higher Rabi frequency. The simplicity of the information processing and alleviation of the bandwidth problem are the main advantages of this proposal in comparison with Ref. [3]. Let us consider a ‘charge’ qubit made of double quantum dot [8] occupied by a single electron, described by Microelectronics Journal 36 (2005) 253–255 www.elsevier.com/locate/mejo