Generation and applications of amplitude-squeezed states of light from semiconductor diode lasers

We describe recent experiments on generation and applications of amplitude-squeezed states of light from a semiconductor diode laser. Amplitude-squeezed light with intensity noise 2 dB below the standard shotnoise limit was observed from a diode laser with a weak optical feedback from an external grating. Applications of this amplitude-squeezed light as a local oscillator in heterodyne detection in Doppler velocity measurement and weak light-scattering measurement are discussed. 1997 Optical Society of America OCIS code: (270.6570) Squeezed states; (140.2020) Diode lasers.


Introduction
Amplitude-squeezed states (or photon-number squeezed states) of light [1,2] have less quantum fluctuations in photon numbers of the light fields than the photon number fluctuatons of coherent states with Poissonian statistics.A photon number state can be considered as an idea single-mode amplitude-squeezed state.When detected by a photodetector, the mean square noise <in 2 > in the photocurrent is suppressed below the standard shot-noise limit (2e 2 η<I>B), where <I> is the mean intensity of the amplitude-squeezed light (in the unit of photons per second), η the quantum efficiency of the photo-detector, and B the bandwidth of the detector system.Unlike squeezed vacuum states [3], amplitudesqueezed states of light can have intense optical power (e.g. a few tens of milliwatts), which allows a direct replacement of coherent lasers in precision optical measurements where quantum shot-noise associated with the laser field needs to be suppressed.Amplitudesqueezed states of light have been successfully generated both from pump-noise-suppressed semiconductor lasers [1,[4][5][6][7][8] and from second-harmonic generation (SHG) process [9][10][11][12][13].Amplitude-squeezed states generated from a pump-noise-suppressed semiconductor laser (which must have a high quantum efficiency of conversion from pumping electron stream to output photon stream) have large squeezing bandwidths, intermediate optical power, and rich wavelengths.By using some line-narrowing techniques such as injection-locking to an external tunable master laser [5] or dispersive optical feedback from an external grating cavity [6,7], the multiple sub-threshold longitudinal side modes in the laser diodes can be effectively suppressed, and, therefore, collimated amplitude-squeezed laser fields with a squeezing typically up to 3-dB or more [14] were generated from the diode lasers.
The applications of squeezed vacuum states and amplitude-squeezed states have also been experimentally demonstrated to improve the sensitivity of precision optical measurements beyond the shot-noise-limit [15][16][17][18][19].For example, squeezed vacuum states have been used to improve the precision of shot-noise limited measurements of weak absorption and in an interferometer [15][16][17].A frequency-tunable squeezed light source has been used to demonstrate improvement in the sensitivity of saturation spectroscopy of atomic cesium and to demonstrate fundamental phenomena in the atom-photon interactions [18].Conversion of amplitude-squeezed states to squeezed vacuum states has also been proposed [19].Several experiments were carried out showing that amplitude-squeezed light from diode lasers can be used to improve the sensitivities of spectroscopic measurements [21][22][23].
In this paper, we present in details our recent experiments on the generation of amplitude-squeezed light from a semiconductor diode laser with a weak optical feedback from a highly dispersive grating in a simple configuration and, then, on applications of the amplitude-squeezed light as a local oscillator in sub-shot-noise Doppler velocity measurement [24] and weak light scattering measurement.In our experiments, the squeezed laser source was a quantum-well AlGaAs semiconductor laser with a weak optical feedback from a grating in a Littman-Metcalf configuration.The maximum feedback intensity was a small fraction (1.2×10 -3 ) of the output power of the laser diode.Since the feedback beam passes the grating twice, the external cavity in this configuration is highly dispersive and, therefore, is effective in suppressing longitudinal side modes.This configuration keeps the advantages of low optical loss for the squeezed-light output and provides frequency tunability [25].Up to 2-dB squeezing over the frequency range from 0.3 MHz to 20 MHz was observed.We then discuss the applications of this amplitude-squeezed light source as a local oscillator for the heterodyne detection of Doppler-shifted light scattered from a gas flow.

Experimental setup
The experimental setup for generating amplitude-squeezed states of light from a semiconductor diode laser is shown in Fig. 1.The laser diode (SDL-5411-G1) and the collimation lens were cooled down to 80 K inside a liquid nitrogen cryostat to increase the electron-to-photon conversion efficiency.Due to the presence of multiple sub-threshold longitudinal side modes in the laser diode, some line-narrowing techniques (such as injection locking or optical feedback from an external grating) must be used in order to obtain amplitude squeezing [5][6][7].Since phase noise of the laser diode is very sensitive to wavelength-selected optical feedback, a weak optical feedback strength is enough to effectively suppress the longitudinal side modes.In our experiment, we used a hightransmission beamsplitter BS (with a transmission of 95%) to reflect a small portion of the laser beam to a grating (1800 lines/mm).The first-order diffracted beam was reflected and fed back to the laser diode by a PZT-controlled mirror.A power meter behind the beamsplitter was used to measure the feedback intensity.The maximum feedback intensity was a fraction (1.2×10 -3 ) of the output power of the laser diode.A neutral density filter (NDF) is used to control the feedback intensity.The threshold current (3.5 mA at 80 K) was not changed significantly by this weak grating feedback.

Measurement of amplitude-squeezing
The output beam of the squeezed light source was detected with two large area pin photodiodes (Hamamatsu S3994), as shown in Fig. 1.A 50% non-polarization beamsplitter was used to divide the squeezed light into two detectors (balanced detection configuration).
The sum or difference of photocurrent noises are measured with a spectrum analyzer, where the sum gives the noise of the output squeezed light and the difference gives the shot-noise level with the same dc photocurrents.An alternate method is to use a single large area pin photodiode to measure the noise of the output laser beam directly.In the later case, a lens was used to expand the laser beam size on the surface of the photodiode such that the laser beam nearly fills the detector aperture in order to prevent the effect of detector saturation at high photocurrents, and the shot-noise level (SNL) was set by a red-filtered white light source with the same dc photocurrent.Great care was taken to check the consistency between the SNL in two identical detectors set by two white light sources and the noise calibrated by the balanced detectors.We found that the noise levels agreed to within 5% for dc detector current up to 15.0 mA per detector for the large beam spot described above.
Figure 2 shows the measured noise power spectral density for the laser beam from the squeezed source, with the laser diode biased at 26.7 mA giving a corresponding photodetector current of 12.0 mA.The feedback intensity was set at the maximum (1.2×10 -3 ).Curve a is the shot-noise level with the same dc photocurrent.Curve c is for the background (amplifier) noise level when the laser beam is blocked.Curve b is for the output beam of the squeezed laser source.It can be seen that wideband squeezing of 2-dB is observed in the frequency range between 0.3 MHz and 20 MHz.
Figure3 shows the measured Fano factor of the output beam from the squeezed laser source at a noise frequency of 10.0 MHz with different bias currents.Fano factor is defined as the ratio between the spectral noise power of the laser field and the shot-noise level at the same dc photocurrent of the detector.Therefore, as the Fano factor is smaller than unity, the laser field shows amplitude-squeezing.The feedback intensity was fixed at its maximum value.From Fig. 3, one can find that, as the bias current of the laser diode is above 3 times the threshold current I th (3.5 mA at the temperature of 80 K), the output beam of the diode laser shows amplitude-squeezing.However, the observed squeezing (or Fano factor) is smaller than the theoretical expected values given by 1-η, where η is the transfer efficiency from the bias current of the laser diode to the dc photocurrent of the detector.This indicates that even with highly dispersive grating feedback, the excess noise in laser diode was not completely suppressed so that the observed squeezing did not reach the optimum values.
Figure 4 shows the dependence of the measured Fano factor on feedback intensity.Again, the observed noise frequency was set at 10.0 MHz and the dc photocurrent was 12.0 mA with the laser diode biased at 26.7 mA.One sees that a weak optical feedback intensity of 1.5×10 -4 is large enough to suppress the amplitude noise of the laser diode below the shotnoise limit.

Applications of amplitude-squeezed light as a local oscillator
Amplitude-squeezed states of light generated from semiconductor lasers have wideband squeezing, intense optical power, and narrow frequency linewidth.They can be used to replace shot-noise-limited laser sources in many applications where ultralow laser noise is required.Here, we will discuss the applications of amplitude-squeezed light as a local oscillator for high sensitive heterodyne detection, for example in sub-shot-noise laser Doppler anemometry and in light scattering measurement.

Sub-shot-noise laser Doppler anemometry
Laser Doppler anemometry is a precise optical technique for measuring velocity of moving particles based on the determination of the Doppler-frequency shift of light scattered from the particles.The small Doppler frequency shifts in the weakly scattered light may be detected by an optical heterodyne technique using a local oscillator beam (or a reference laser beam) such that the velocity and density of moving particles in a fluid can be determined from the beat frequency and the peak height of the beating signal.For the experimental arrangement as shown in Fig. 5, the Doppler shift of the scattered light (dashed line directed to the detector) is given by [26] ν where n is the index of refraction of the flow medium, u is the velocity vector of the flow with amplitude u, λ is the wavelength of the laser beam, k 0 and k s are the unit vectors in the directions of the illuminating and scattering (reference) beams, respectively, and α is the angle between them.The fundamental limitation to sensitivity of this reference beam technique is the shot-noise arising from the reference laser beam [26].The light received by the photodetector comprises a strong local oscillator (reference beam) component and a much weaker Doppler-shifted (scattered light) component.The photocurrent is i(t) ≈ ηe [I lo +2 (I lo I s ) 1/2 cos(2πν D t)], where η is the quantum efficiency of the photodetector, and I lo and I s are the photon number fluxes (intercepted by the detector per unit time) of the reference and scattered beams, respectively.The mean square heterodyne signal current at frequency ν D is then given by <i s (2) From the above equation, it is obvious that an amplitude-squeezed local oscillator beam (with F o <1) leads to enhanced sensitivity of Doppler velocity measurements relative to the shotnoise-limited measurements (with F o =1).The experimental arrangement in Fig. 5 is a typical reference beam heterodyning configuration for laser Doppler measurements [26].The amplitude-squeezed laser beam from the squeezed source (about 25mW at 770 nm) passes through a polarizer (extinction ratio >10 4 :1) and two optical isolators (total isolation ratio >60 dB), and is, then, focused by lens L1 (with f=75 mm) onto the flow; this focused light acts as the illumination beam.The transmitted laser beam, which serves as the reference beam, is collected and focused by lens L2 (with f=100 mm).The reference beam is also focused onto the flow but its focus is slightly displaced from that of the illumination beam.This ensures that the effective scattering regions are slightly different for the two beams and so avoids loss of signals by phase decorrelation [26].The scattered light (dashed line) is focused with the reference beam (LO beam) by another lens and passes through an aperture in front of a high efficiency pin photodiode.The ac part of the photodetector current is amplified and fed into a spectrum analyzer.The gas flow used in the experiment comprised high pressure clean nitrogen gas passing through a small chamber containing a smoke generator.As the smoke passed through the intersection region of the illumination and reference beams, the photodetector current decreased by less than 2%.In order to eliminate possible feedback of scattered light into the squeezed source, we inserted a polarizer and two optical isolators between the squeezed source and the scattering region.The optical feedback due to light scattering by the gas flow was less than 10 -8 .Thus, the optical feedback into the laser diode was dominated by the grating feedback which was set at its maximum feedback intensity of about 1.2×10 -3 .As the polarizer and optical isolators were inserted, the squeezing (about 2-dB) was degraded to about 1.0 dB due to the additional optical losses.However, the total light scattering from the flow is very weak (corresponding to an optically thin medium), the optical loss of squeezed local oscillator beam due to the light scattering is correspondingly small and will not significantly degrade the squeezing of the squeezed LO beam.This is the basis of this new technique.

Light scattering
In the application of sub-shot-noise laser Doppler anemometry, the squeezed local oscillator beam and the illumination laser beam come from the same laser source; they have the same frequency.The scattered light of the illumination beam from the moving particles is frequency-shifted due to Doppler effect.Therefore, the heterodyne beating signal between the squeezed local oscillator and frequency-shifted scattered light appear in the non-zero frequency range where sub-shot-noise fluctuations of the squeezed local oscillator take place.However, in many light scattering experiments, the scattering particles in the transparent media are stationary or moving slowly, which makes the scattered light have almost the same frequency as the illumination beam.In this case, in order to shift the heterodyne beating signal between the squeezed local oscillator and the scattered light to the squeezing frequency range, the illumination beam is required to shift its frequency from the squeezed local oscillator.This can be implemented by using a master laser and an injection-locking semiconductor laser [5].The injection-locked semiconductor laser is used as the squeezed local oscillator and the master laser (after injection-locking) is frequency-shifted (e.g. by an AO modulator) and, then, used as the illumination laser.
The application of squeezed local oscillator in coherent detection of light scattering experiments may improve the sensitivity of optical sensors which base on laser scattering beyond the shot-noise-limit.For example, optical particle counters (OPC) detect individual particles or microscopic dust inside a semiconductor processing chamber by measuring weak scattered light [27].This technique has reached extremely high sensitivity and needs 50 scattered photons to detect a single particle due to the quantum limit [28].By applying squeezed LO to overcome the quantum limit, the scattered photon number required to identify an individual particle would be reduced since the minimum measurable scattered photon flux is given by I s =BF 0 /η from Eq.( 2) assuming that the signal-to-noise ratio is equal to 1. And, therefore, the sensitivity of the OPC will be improved if F 0 <1.

Conclusion
We have discussed our recent experiments on generation and applications of amplitudesqueezed states of light from a semiconductor diode laser.A wideband amplitude-squeezed light with 2.0 dB squeezing was generated from a diode laser (cooled to 80 K in a minicryostat) with a weak optical feedback from an external grating.Dependence of amplitudesqueezing on bias current and feedback intensity was experimentally measured.Application of amplitude-squeezed light as a local oscillator for heterodyne detection was demonstrated in sub-shot-noise laser Doppler anemometry with an improvement of 1.0 dB in the detection signal-to-noise ratio beyond the shot-noise limit.The application of the squeezed local oscillator in light scattering experiments was also discussed.

Fig. 1 Fig. 2
Fig.1 Experimental setup for generation of amplitude-squeezed states of light from a diode laser.The laser diode (LD) and collimating lens are cooled in a cryostat.LD -laser diode; BS -beamsplitter; NDF -neutral density filter; PZT -PZT controlled mirror.

Fig. 3 Measured 8 FFig. 4 Measured
Fig.3Measured Fano factor (at 10.0 MHz) of the diode laser at different bias currents.The feedback intensity was set at the maximum value and the threshold current Ith was 3.5 mA at 80 K. η is the transfer efficiency from the bias current of the laser diode to the dc photocurrent of the detector.

2 > 2 >/ <i n 2 >
= 2 e 2 η 2 I s I lo and the mean square noise current by <i n 2 > = 2 e 2 η I lo B F o with B the noise bandwidth, and F o the Fano factor of the detected local oscillator beam.The signal-to-noise ratio is then given by <i s = η I s / (B F o ) .

Fig. 6 .
Fig. 6.Measurements of Doppler shift signals at different nitrogen gas pressures.The flow velocities were inferred to be (a) 32.4 cm/s, and (b) 26.7 cm/s.The dc detector current is 10.0 mA.The spectrum analyzer was set with a resolution bandwidth of 30 kHz, a video bandwidth of 100 Hz, and a scan time of 2.0s.

Figure 6
Figure 6 shows the experimental results of our Doppler velocity measurements.The flow velocities of 32.4 cm/s and 26.7 cm/s were inferred from the observed Doppler shift signals in Fig. 6(a)-(b), respectively.The minimum measurable Doppler-shift signals were found clearly below that set by the conventional shot-noise level.