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arXiv:quant-ph/0505164 · Journal of Optics B Quantum and Semiclassical Optics

Quantum noise locking

Kirk McKenzie, Eugeniy E. Mikhailov, Keisuke Goda, Ping Koy Lam, Nicolai B. Grosse, Malcolm B. Gray, N. Mavalvala, David E. McClelland

Published Sep 26, 2005• 87 citations
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Abstract

Quantum optical states which have no coherent amplitude, such as squeezed vacuum states, can not rely on standard readout techniques to generate error signals for control of the quadrature phase. Here we investigate the use of asymmetry in the quadrature variances to obtain a phase-sensitive readout and to lock the phase of a squeezed vacuum state, a technique which we call noise locking (NL). We carry out a theoretical derivation of the NL error signal and the associated stability of the squeezed and anti-squeezed lock points. Experimental data for the NL technique both in the presence and absence of coherent fields are shown, including a comparison with coherent locking techniques. Finally, we use NL to enable a stable readout of the squeezed vacuum state on a homodyne detector.

DOI
10.1088/1464-4266/7/10/032

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We study the steady-state operation and noise properties of a laser (or maser) exhibiting phase locking when an ordinary vacuum is replaced by a squeezed vacuum. Such a phase-sensitive laser can be realized by preparing the active medium initially in a coherent superposition of levels involved in the laser transition. We develop a general formalism to treat number-phase fluctuations and quadrature fluctuations. When applied to a one-photon laser with injected atomic coherence, we find that not only is a complete quenching of the (spontaneous-emission) quantum noise possible, but the field can actually be in a squeezed state. The variance in either amplitude or phase quadrature can be below the vacuum noise level by a factor of 2 (50%) at the expense of enhanced fluctuations in the other quadrature.
Squeezed states of light produced by nonlinear interactions in periodically poled crystals are specially engineered quantum states where the uncertainties in the phase or amplitude quadrature can be traded against each other. These low-noise states have applications in quantum communication, sensing, and computing [1]. To fully exploit these applications, precise phase locking of the squeezed light to a local oscillator (LO) phase is essential. For single-pass waveguides the used locking technique has relied on the injection of a frequency-shifted input seed to generate the error signal [1]. Here we assess the advantages and challenges of implementing a technique originally devised for cavity-based squeezed light sources called quantum noise locking (QNL) [2], which features a simplified feedback structure, eliminating the need for an additional frequency shifted field, thereby avoiding seeding and extra optical components. This work experimentally extends QNL to periodically poled LiNbO3waveguides for the first time, which allows for phase controlled squeezing, with less than 10 mrad phase noise, over a 50 GHz bandwidth.
Quantum noise will be the dominant noise source for the advanced laser interferometric gravitational wave detectors currently under construction. Squeezing-enhanced laser interferometers have been recently demonstrated as a viable technique to reduce quantum noise. We propose two new methods of generating an error signal for matching the longitudinal phase of squeezed vacuum states of light to the phase of the laser interferometer output field. Both provide a superior signal to the one used in previous demonstrations of squeezing applied to a gravitational-wave detector. We demonstrate that the new signals are less sensitive to misalignments and higher order modes, and result in an improved stability of the squeezing level. The new signals also offer the potential of reducing the overall rms phase noise and optical losses, each of which would contribute to achieving a higher level of squeezing. The new error signals are a pivotal development towards realizing the goal of 6 dB and more of squeezing in advanced detectors and beyond.
Quantum noise will be the dominant noise source for the advanced laser interferometric gravitational wave detectors currently under construction. Squeezing-enhanced laser interferometers have been recently demonstrated as a viable technique to reduce quantum noise. We propose two new methods of generating an error signal for matching the longitudinal phase of squeezed vacuum states of light to the phase of the laser interferometer output field. Both provide a superior signal to the one used in previous demonstrations of squeezing applied to a gravitational-wave detector. We demonstrate that the new signals are less sensitive to misalignments and higher order modes, and result in an improved stability of the squeezing level. The new signals also offer the potential of reducing the overall rms phase noise and optical losses, each of which would contribute to achieving a higher level of squeezing. The new error signals are a pivotal development towards realizing the goal of 6 dB and more of squeezing in advanced detectors and beyond.
In this thesis an alternative method to stabilize the phase of a squeezed vacuum field in the framework of the Virgo gravitational wave detector is designed and realized. A brief introduction about the nature of gravitational waves and their detection is presented in chapter 1, with particular attention to the actual sensitivity limitations on the interferometers employed. Chapter 2 focuses on the quantum nature of the electromagnetic field. A nonclassical state of the light, the squeezed state, is described, as well as how it is is produced and how can be observed. This kind of radiation field is employed to increase the sensitivity of the detectors beacause with its injection into the interferometer the quantum noise that affects the measure is partially reduced. In order to avoid any technical noise contamination, a second copropagating and frequency shifted field is used to provide the error signal for the alignment and to allow the phase locking between the interferometer main laser and the squeezed light, as discussed in chapter 3, where the technique called coherent control loop is explained. Finally, in chapter 4, the optical bench and the control electronics realized at LNL to test the stability of the control loop are presented; the system will be implemented in Virgo in the next months. The difference between the method discussed here and that usually employed is that the error signal is not used to correct the path of the squeezed vacuum field, but it is instead used to close a cascade loop on a PLL. Thus all the actuators are electronic and no optical actuators are used, the stray light issue is minimized. The control loop is stronger at low frequencies in order to correct the seismic noise that dominates in this region.
The balanced homodyne detection technique is an important method to detect the quantum light field. The signal light injected into the phase sensitive optical parameter amplifier (OPA) is phase modulated. The output squeezed light of OPA is detected by the balanced homodyne detection system. When the phase sensitive OPA is operated at parametric amplification and deamplification respectively, we can judge which quadrature component of the quantum light field is measured by observing the modulation signal. We can demodulate the phase modulation signal to achieve the error signal, which is used to lock the relative phase of zero between the local and the quantum light fields (corresponding to the quadrature-amplitude of the unknown light field).