Optical coherence and teleportation: Why a laser is a clock, not a quantum channel

It has been argued [T. Rudolph and B.C. Sanders, Phys. Rev. Lett. {\bf 87}, 077903 (2001)] that continuous-variable quantum teleportation at optical frequencies has not been achieved because the source used (a laser) was not `truly coherent'. Van Enk, and Fuchs [Phys. Rev. Lett, {\bf 88}, 027902 (2002)], while arguing against Rudolph and Sanders, also accept that an `absolute phase' is achievable, even if it has not been achieved yet. I will argue to the contrary that `true coherence' or `absolute phase' is always illusory, as the concept of absolute time on a scale beyond direct human experience is meaningless. All we can ever do is to use an agreed time standard. In this context, a laser beam is fundamentally as good a `clock' as any other. I explain in detail why this claim is true, and defend my argument against various objections. In the process I discuss super-selection rules, quantum channels, and the ultimate limits to the performance of a laser as a clock. For this last topic I use some earlier work by myself [Phys. Rev. A {\bf 60}, 4083 (1999)] and Berry and myself [Phys. Rev. A {\bf 65}, 043803 (2002)] to show that a Heisenberg-limited laser with a mean photon number $\mu$ can synchronize $M$ independent clocks each with a mean-square error of $\sqrt{M}/4\mu$ radians$^2$.Comment: 14 pages, no figures, some equations this time. For proceedings of SPIE conference "Fluctuations and Noise 2003

Phase measurements at the theoretical limit

It is well known that the result of any phase measurement on an optical mode made using linear optics has an introduced uncertainty in addition to the intrinsic quantum phase uncertainty of the state of the mode. The best previously published technique [H. M. Wiseman and R.B. Killip, Phys. Rev. A 57, 2169 (1998)] is an adaptive technique that introduces a phase variance that scales as n^{-1.5}, where n is the mean photon number of the state. This is far above the minimum intrinsic quantum phase variance of the state, which scales as n^{-2}. It has been shown that a lower limit to the phase variance that is introduced scales as ln(n)/n^2. Here we introduce an adaptive technique that attains this theoretical lower limit.Comment: 9 pages, 5 figures, updated with better feedback schem

Selective linear or quadratic optomechanical coupling via measurement

The ability to engineer both linear and non-linear coupling with a mechanical resonator is an important goal for the preparation and investigation of macroscopic mechanical quantum behavior. In this work, a measurement based scheme is presented where linear or square mechanical displacement coupling can be achieved using the optomechanical interaction linearly proportional to the mechanical position. The resulting square displacement measurement strength is compared to that attainable in the dispersive case using the direct interaction to the mechanical displacement squared. An experimental protocol and parameter set are discussed for the generation and observation of non-Gaussian states of motion of the mechanical element.Comment: 7 pages, 2 figures, (accepted in Physical Review X

Adaptive Quantum Measurements of a Continuously Varying Phase

We analyze the problem of quantum-limited estimation of a stochastically varying phase of a continuous beam (rather than a pulse) of the electromagnetic field. We consider both non-adaptive and adaptive measurements, and both dyne detection (using a local oscillator) and interferometric detection. We take the phase variation to be \dot\phi = \sqrt{\kappa}\xi(t), where \xi(t) is \delta-correlated Gaussian noise. For a beam of power P, the important dimensionless parameter is N=P/\hbar\omega\kappa, the number of photons per coherence time. For the case of dyne detection, both continuous-wave (cw) coherent beams and cw (broadband) squeezed beams are considered. For a coherent beam a simple feedback scheme gives good results, with a phase variance \simeq N^{-1/2}/2. This is \sqrt{2} times smaller than that achievable by nonadaptive (heterodyne) detection. For a squeezed beam a more accurate feedback scheme gives a variance scaling as N^{-2/3}, compared to N^{-1/2} for heterodyne detection. For the case of interferometry only a coherent input into one port is considered. The locally optimal feedback scheme is identified, and it is shown to give a variance scaling as N^{-1/2}. It offers a significant improvement over nonadaptive interferometry only for N of order unity.Comment: 11 pages, 6 figures, journal versio