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Physical Review A

Quantum noise properties of an injection-locked laser oscillator with pump-noise suppression and squeezed injection

L. Gillner, Gunnar G. Bjork, Y. Yamamoto

Published May 1, 1990• 35 citations
Publisher

Abstract

The quantum noise properties of injection-locked semiconductor laser oscillators are investigated. Included in the analysis are pump-noise suppression and squeezing of the injection signal. It is shown that the main effect of injection locking is the reduction of the phase noise of the outgoing laser light field. The influence that squeezing of the injection signal state has on the output state is shown to be strongly dependent on the value of the linewidth enhancement factor. In general, little or no noise reduction stands to be gained by squeezing the injection signal. It is also shown that under idealized conditions, the spectral uncertainty product of the outgoing field will approach, but never go below, the minimum uncertainty value given by the Heisenberg uncertainty relation.

DOI
10.1103/physreva.41.5053

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The quantum noise properties of injection-locked semiconductor laser oscillators are investigated. Included in the analysis are pump-noise suppression and squeezing of the injection signal. It is shown that the main effect of injection locking is the reduction of the phase noise of the outgoing laser light field. The influence that squeezing of the injection signal state has on the output state is shown to be strongly dependent on the value of the linewidth enhancement factor. In general, little or no noise reduction stands to be gained by squeezing the injection signal. It is also shown that under idealized conditions, the spectral uncertainty product of the outgoing field will approach, but never go below, the minimum uncertainty value given by the Heisenberg uncertainty relation.
This paper clarifies the origins of the standard quantum limit for the amplitude noise of a laser-oscillator outgoing field. The amplitude noise within the cavity bandwidth, \ensuremath{\Omega}\ensuremath{\le}\ensuremath{\omega}/Q, is ultimately caused by the pump amplitude fluctuation, while that above the cavity bandwidth, \ensuremath{\Omega}\ensuremath{\ge}\ensuremath{\omega}/Q, is due to the field zero-point fluctuation. The uncertainty product of the amplitude- and phase-noise spectra at an extremely high pumping level is still larger than the Heisenberg minimum-uncertainty product because of the presence of nonstationary phase-diffusion noise. In this sense, an ordinary laser oscillator is not a quantum-limited device. This paper suggests that a laser oscillator can produce an amplitude-squeezed state in itself if the pump amplitude fluctuation is suppressed below the ordinary shot-noise level. The paper discusses possible schemes for suppressing pump fluctuation, commutator bracket preservation without pump fluctuation, and resulting amplitude and phase spectra. The similarity of and difference between a pump-noise-suppressed laser and a cavity degenerate parametric amplifier are delineated.
This thesis describes the phase and amplitude noise properties of semiconductor lasers subjected to weak, dispersive optical feedback. In the first half, experiments demonstrating reductions in the laser frequency noise power spectrum and spectral linewidth by several orders of magnitude are presented. Weak optical feedback is applied to the laser by an external cavity containing an atomic vapor. The presence of the vapor adds to the dispersion of the cavity and simultaneously locks the laser to a fixed frequency reference. The role of 1/f frequency noise in limiting the effectiveness of this linewidth reduction technique is investigated and 1/f noise is found to be the dominant contribution to the linewidth under strong optical feedback conditions. An electronic feedback scheme utilizing FM sideband locking is then implemented alongside the optical feedback, and an additional reduction in the low frequency 1/f frequency noise power spectrum by over two orders of magnitude is obtained. With both systems operating simultaneously, the spectral linewidth is narrowed from its free-running value of about 20 MHz to 1.4 kHz. Excellent absolute frequency stability is also achieved. In the second half, the effects of optical feedback on the quantum mechanical amplitude noise properties of the laser are examined. A fully quantum mechanical theory of amplitude and phase noise for a semiconductor laser with weak optical feedback is developed, and the nature and limits of the noise reduction using this technique are established. Particular attention is given to the feedback-induced enhancement of the amplitude squeezing which can be obtained in a pump-suppressed semiconductor laser: an improvement in the squeezing by 3 dB is predicted under moderate pumping. Somewhat larger noise reductions are expected when the laser is operating closer to threshold. Measurements performed on a laser biased close to threshold are then described and a reduction in the low frequency amplitude noise power spectrum by 7 dB is obtained. An experimental investigation of the effects of optical feedback on the amplitude squeezing in a semiconductor laser is then discussed. The low frequency squeezing in a room temperature device is increased from 3% below the standard quantum limit (SQL) under free-running conditions to 19% below the SQL with optimal feedback. The experimental results are found to agree poorly with the single-mode model and a multi-mode model including the effects of asymmetrical cross-mode non-linear gain is developed to explain the discrepancy. Finally, further experimental investigation into the generation of amplitude squeezed light is presented using a commercial laser with no intentional external modifications. Squeezing as large as 29% below the SQL is measured using a balanced homodyne detector with the laser operating near room temperature, corresponding to 41% below the SQL at the output facet of the laser.
The search for ever quieter light sources has fueled experimental interest in the noise properties of injection locked lasers [ 1,2,3], Ref. 1 showed that the injection of a small signal into a pump noise suppressed semi-conductor laser could suppress small longitudinal side modes whilst leaving the non-classical noise characteristics of the free running laser unaffected. In contrast [2] and [3] found that in Nd:YAG lasers the free running noise characteristics were suppressed and the output noise was an amplified version of the injected signal.
The intensity-noise properties of an injection-locked semiconductor laser were studied experimentally. The constant-current-driven semiconductor laser producing the amplitude-squeezed state whose intensity noise was reduced below the standard quantum limit (SQL) by 0.72 dB was injection-locked by an external master laser. The measured intensity-noise level of the injection-locked semiconductor laser was 0.91 dB below the SQL. This experimental result indicates that a phase-coherent amplitude-squeezed state or squeezed vacuum state together with a reference local oscillator wave can be generated directly by semiconductor laser systems.
The influence of injected atomic coherence on a laser's operation is discussed by analyzing the semiclassical equations of motion of this system. Both stationary-steady-state and time-dependent regimes of operation are investigated. We present the dependence of the stationary laser intensity and phase on the external parameters (population inversion, amplitude of atomic coherence, and detuning). For small cavity-field detuning and large atomic coherence, both frequency and phase locking occurs. The laser frequency is locked to the atomic frequency, and the phase is locked to a value determined primarily by the phase of the atomic coherence. Under certain conditions, in the inverted regime, the output intensity is an ssS-shaped function of the atomic coherence, leading to the possibility of a bistable behavior. However, only a portion of the bistable curve gives stable stationary operation, and in critical points (the location of which depends crucially on the external parameters) time-dependent instabilities branch away. When the detuning is larger than a critical value there is neither phase nor frequency locking. We find that the time-dependent behavior of the laser intensity in this case is oscillatory (quasiperiodic), and show that there is a stable limit cycle in the phase plane of the quadratures. There is a small parameter region where a stationary steady state and an oscillatory state may coexist. We also consider the nonlinear quantum theory of a laser with injected atomic coherence, and include the effect of pumping statistics. We derive the Fokker-Planck equation for the P representation, and express the noise in terms of moments. We find that in the steady state the intensity noise can be suppressed below the shot-noise limit but that the phase fluctuations are not affected by pump regularity. For nonzero detuning, we find that transient squeezing of the phase fluctuations is possible.
Experimental investigations illustrating the intensity noise properties of injection-locked solid-state lasers were performed. The measured results are predicted by a quantum mechanical model. The theory describes the intensity noise transfer to the slave laser’s output for large modulation signals as well as for signals at the quantum noise level. Different frequency regions in the intensity noise spectrum are identified and it is shown that there exist different minimum noise levels in these regions. Under appropriate conditions, injection-locked lasers can generate non-classical light.