Topics in modeling, analysis and simulation of near-term quantum physical systems with continuous monitoring

In this work, we study two important problems in the quantum world: single-photon source and single-spin measurement.;Single-photon source. We consider a quantum dot that is inside a cavity operating in a weak coupling regime. We model the system in the cavity QED setting and use Jayes-Cummings Hamiltonian to describe the dot-cavity interaction. The decoherence effects that we consider include spontaneous emission, cavity leakage and dephasing, along with continuous monitoring of the dot; we describe the system using a stochastic master equation. There are 2 measure of 'goodness' for a single-photon state---|indistinguishability and single-photon probability. 1. Indistinguishability: We propose an engineering technique using continuous quantum measurement in conjunction with feed forward to improve indistinguishability of a single-photon source. The technique involves continuous monitoring of the state of the emitter, processing the noisy output signal with a simple linear estimation algorithm, and feed forward to control a variable delay at the output. In the weak coupling regime, the information gained by monitoring the state of the emitter is used to reduce the time uncertainty inherent in photon emission from the source, which improves the indistinguishability of the emitted photons. 2. Single-photon probability: An engineering technique using continuous quantum measurement in conjunction with a change detection algorithm is proposed to improve probability of single photon emission for a quantum-dot based single-photon source. The technique involves continuous monitoring of the emitter, integrating the measured signal, and a simple change detection circuit to decide when to stop pumping. The idea is to pump just long enough such that the emitter + cavity system is in a state that can emit at most 1 photon with high probability. Continuous monitoring provides partial information on the state of the emitter. This technique is useful when the system is operating in the weak coupling regime, and the rate of pumping is smaller than, or comparable to, the emitter-cavity coupling strength, as can be the case for electrical pumping.;Single-spin measurement. A promising technique for measuring single electron spins is magnetic resonance force microscopy (MRFM), in which a microcantilever with a permanent magnetic tip is resonantly driven by a single oscillating spin. The most effective experimental technique is the OScillating Cantilever-driven Adiabatic Reversals (OSCAR) protocol, in which the signal takes the form of a frequency shift. If the quality factor of the cantilever is high enough, this signal will be amplified over time to the point that it can be detected by optical or other techniques. An important requirement, however, is that this measurement process occur on a time scale short compared to any noise which disturbs the orientation of the measured spin. We describe a model of spin noise for the MRFM system, and show how this noise is transformed to become time-dependent in going to the usual rotating frame. We simplify the description of the cantilever-spin system by approximating the cantilever wavefunction as a Gaussian wavepacket, and show that the resulting approximation closely matches the full quantum behavior. We then examine the problem of detecting the signal for a cantilever with thermal noise and spin with spin noise, deriving a condition for this to be a useful measurement.