General Formalism for Evaluating the Impact of Phase Noise on Bloch Vector Rotations

Quantum manipulation protocols for quantum sensors and quantum computation often require many single qubit rotations. However, the impact of phase noise in the field that performs the qubit rotations is often neglected or treated only for special cases. We present a general framework for calculating the impact of phase noise on the state of a qubit, as described by its equivalent Bloch vector. The analysis applies to any Bloch vector orientation, and any rotation axis azimuthal angle for both a single pulse, and pulse sequences. Experimental examples are presented for several special cases. We apply the analysis to commonly used composite $\pi$-pulse sequences: CORPSE, SCROFULOUS, and BB1, used to suppress static amplitude and detuning errors, and also to spin echo sequences. We expect the formalism presented will help guide the development and evaluation of future quantum manipulation protocols.Comment: 12 pages, 6 figures, submitted to PR

Relaxation oscillations, stability, and cavity feedback in a superradiant Raman laser

We experimentally study the relaxation oscillations and amplitude stability properties of an optical laser operating deep into the bad-cavity regime using a laser-cooled $^{87}$Rb Raman laser. By combining measurements of the laser light field with nondemolition measurements of the atomic populations, we infer the response of the gain medium represented by a collective atomic Bloch vector. The results are qualitatively explained with a simple model. Measurements and theory are extended to include the effect of intermediate repumping states on the closed-loop stability of the oscillator and the role of cavity feedback on stabilizing or enhancing relaxation oscillations. This experimental study of the stability of an optical laser operating deep into the bad-cavity regime will guide future development of superradiant lasers with ultranarrow linewidths.Comment: 9 pages, 6 figure