Observation of sub-poissonian light in parametric downconversion

Observation of sub-poissonian light in parametric downconversion

Volume 62, number 3 OPTICS COMMUNICATIONS 1 May 1987 OBSERVATION OF S U B - P O I S S O N I A N L I G H T IN PARAMETRIC D O W N C O N V E R S I O N...

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Volume 62, number 3

OPTICS COMMUNICATIONS

1 May 1987

OBSERVATION OF S U B - P O I S S O N I A N L I G H T IN PARAMETRIC D O W N C O N V E R S I O N J.G. RARITY, P.R. TAPSTER and E. JAKEMAN Royal Signals and Radar Establishment, Malvern, Worcestershire WR14 3PS, UK

Received 25 November 1986; revised manuscript received 27 January 1987

We report the first observation of sub-poissonianphoton statistics for light generated by the use of a detection triggeredoptical shutter in parametric downconversion. A normalised second factorial moment of the photon counting distribution of 0.42 has been achieved with a pre-detection Fano factor of 0.984.

The generation of light with properties that cannot be predicted without quantizing the Maxwell field is of interest both from a fundamental point of view and in the context of improved measurement accuracy [ 1,2]. Various proposals have been made for the use of squeezed states in signal processing [ 3,4 ] and interferometry [ 5 ], whilst the more readily appreciated photon antibunching and sub-poissonian statistics would also appear to have useful practical applications [ 6,7 ] and certainly interesting experiments on the fundamental nature of light can be envisaged [ 8,9 ]. Thus there is currently a great deal of effort being devoted to devising experiments which generate non-classical light. Earlier experiments have shown some success in achieving a small degree of antibunching or small reduction in photon counting fluctuations below that expected for a Poisson process [ 10-13 ], while recent squeezing experiments have also produced sub-poissonian effects [14], These experiments are based on a variety of mechanisms ranging from single atom resonance fluorescence to the Franck-Hertz effect and no doubt other proposals made in the literature are currently being tested [ 15-18 ]. In recent papers the use of optical shutters to generate non-classical light in parametric downconversion was proposed [ 19 ], evaluated [ 20] and small antibunching effects observed in a preliminary experimental investigation [ 13 ]. In this paper a modified version of the experiment is described which yields light with significantly reduced factorial moments by comparison with those o f a Poisson dis-

tribution, and a discernable reduction in Fano factor (i.e. shot noise variance). These experiments exploit the fact that two identical trains of photons are produced in a suitably configured parametric downconversion apparatus and use detection of photons in one train to optically gate photons in the other train. The potential of this approach for noise reduction is large because the source is partially collimated. Previous experimental realisations of sub-poissonian sources [ 11,12] emit into 4n steradians and detection efficiencies are limited by the geometry of the collection optics. We emphasise here that we have created a subpoissonian light source which then, on detection, gives the rise to sub-poissonian photoelectron statistics. Large apparent noise reductions have also been seen in closed loop shutter experiments [ 19,21 ] but in such systems the noise reduced light is not available for use. Such experiments can be analysed using semi-classical theories [ 22 ]. In contrast we note that this experiment is the first practical demonstration of the use of a quantum non-demolition measurement [ 16] of photon number to reduce the shot noise of a source. Furthermore this source is in principle a source of localised one-photon states as discussed in refs. [ 8 ] and [ 9 ]. In these previous experiments, onephoton states were inferred by post-detection coincidence gating while here we utilise an optical shutter to select single photons and introduce a dead time between shutter open events to produce an antibunched and sub-poissonian photon beam. Such a

201

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OPTICS COMMUNICATIONS

TRIGSERCHANNEL PHOTODIOOE F-----

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1 May 1987

that the signal detector is 100% efficient the number of counts per sample in the signal channel is given by

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where m is drawn from a Poisson distribution of mean ( 1 - r h ) / ~ t , rh being the trigger detector efficiency and/~ the ideal detection rate of pairs in the absence of shutters etc. It is not difficult to show that the normalised second factorial moment of the photocount n can be expressed in the form n (2) = / 2

Fig. 1. Schematicdiagram of apparatus.

one-photon source is suitable for amplification to a (higher intensity) n-photon source using a suitable optical amplification scheme [ 17 ]. The principle of the experiment can be understood from the schematic diagram shown in fig. 1 which is a modified version of the configuration investigated previously by Walker and Jakeman [ 13,19,20]. A birefringent non-linear crystal arranged for nondegenerate parametric downconversion is illuminated by a UV laser source. Splitting of incident UV photons takes place within the non-linear crystal and the pairs of angularly resolved red photons so produced are observed by the (photon counting) trigger and signal detectors. At the trigger detector an electronic deadtime ZD is introduced so that detection events in this channel are at least TD apart. When each of these events is registered a shutter is opened for a short time t in the signal channel. An optical delay is included before the shutter in this channel to compensate for electronic and shutter response times, etc. Thus only the partners of events actually registered in the trigger channel should be observed in the signal channel. In principle this overcomes the problem of random partnerless events arising in the signal channel due to the low efficiency of the trigger channel detector, which considerably reduced the nonclassical effects observed in the earlier experiment [ 13 ]. The ideal signal is thus a 0-1 random variable. In practice, there is always the chance of observing further events in the signal channel during the finite open time t. In order to investigate this effect we suppose that the number of open intervals per sample time Tis Nwith t<< T, ZD" Assuming for the moment 202

2

X

_(m> l + - - 2 + < m > (2) 1+ ( l + < m > ) 2 _ ] ( l + )2 •

This quantity is not affected by the low efficiency of the detection system in the signal channel. The reduction in measured signal variance over the conventional Poisson variance, the Fano factor F, is however dependent on signal channel quantum efficiency. By definition F=(Varn)/=l+

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(3)

where = r / 2 ( N ) (1 + ) and n (2) is given by eq. (2). In the current experiment detector efficiency is only 2% so that even if the predetection Fano factor is small an observed Fano factor of 0.98 is to be expected at best. On the other hand the second factorial moment is minimised by choosing T < zD when the first term in eq. (2) vanishes. Since from the theory of deadtimes [ 23,24 ] = r h R T / ( l +rh/~rD) we can write in this case

(25)

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with y = qIRrD and 7* = rh/~ T. Clearly, for small n (2) we need TD,~ T, yt]'CD<
Volume 62, number 3

OPTICS COMMUNICATIONS

the effective efficiencies rh and ~/2 appearing in eqs. (3) and (4). In the experiment, a KD*P crystal illuminated by a helium/cadmium laser (lasing at 325 nm wavelength) was used; tilted until the red down-converted photons could be observed separated in direction by approximately 10 degrees (crystal axis at approximately 60 degrees to the incident UV beam). For maximum trigger channel efficiency a silicon avalanche photodiode (APD: RCA type 30921S) was used. Single photon counting was achieved by biasing the APD beyond breakdown and passively quenching the photoelectron triggered avalanches with a 330 k,Q series resistor [26]. Suitable discriminator circuitry, measuring across a further small (50 12) series resistance, was used to produce, as output, a train of standardised photoelectron pulses. The APD was cooled to a constant temperature, typically - 3 degree Celsius, using a thermoelectric cooler. When operated 25 V beyond breakdown a dark count rate of about 12 kHz was measured. At this relatively high over-voltage the device quantum efficiency has reached a saturation value around 25% (at these wavelengths) and count rate drift due to temperature fluctuation (upto + / - 0 . 5 degrees Celsius) is negligible. The optical delay consisted of 170 m of multimode optical fibre, of core diameter 50/tin and numerical aperture (NA) 0.23 (measured at 830 nm), producing a delay of 0.9 #s. Light was launched into this fibre using a 0.2 NA microscope objective placed 30 cm from the crystal. At the output end of the fibre a × 15 magnification system transferred an image of the fibre end to a fast acousto-optical switch (Automates et Automatismes type AAMT-08). The first order Bragg spot could be switched on after a delay of about 0.6/is with a rise time faster than 120 ns (10% to 90% points). An extinction ratio better than 250:1 was obtained on using an aperture to select out this first order beam. The first order image of the fibre end was then reimaged onto the photocathodes of two cooled conventional photon counting photomultiplier (PMT) systems (Malvern Instruments type RF313) via a pellicle beamsplitter. Photon counting PMT's were used because of their intrinsically low dark count. The standardised pulse outputs from the PMT's and the APD discriminator could be fed to a digital correlator (Malvern Instruments K7023). The

1 May 1987

correlator operates as a multichannel delayed coincidence counter when used in cross-correlation mode at its shortest sample time (50 ns, also the deadtime of the discriminator circuitry). Conjugate photon trains were selected by fibre input and trigger detector apertures combined with long wavelength transmitting colour glass filters (cut-off below 600 nm wavelength), to remove UV flare and fluorescence. Aperture positions were optimised by maximising the coincidence count rates between the two channels (PMT versus APD) with the shutter held open. The mean coincidence count rate g is given by c= ~/1 ~/2/~,

(5)

and using the mean count rates in the trigger fit=rhk, and signal fi=r/2/~ detectors the quantum efficiencies ql and q2 can be measured. Optimum values obtained using this apparatus were q~ =0.09 with q2 = 0.0006. This suggests optical and alignment losses greater than a factor of 2 in the trigger channel (theoretical r/l ~0.25) and a factor of I0 loss in the fibre and shutter (PMT quantum efficiency=0.02, alignment loss × 2, beamsplitter × 2). After alignment the shutter-open-pulse delay was adjusted to match the fibre-optic delay and the deadtime between shutter open events introduced. The second factorial moment n (2) and the autocorrelation function of the signal channel light were estimated from the normalised cross-correlation gtx 2) ( z ) of the PMT outputs, g~(~) =

T (n, >r T

=g(2)(r), =~/(2)T,

r#0, ~=0,

n~ and n2 are respectively photocounts from the detectors in sample time T, g(2) (z) is the normalised intensity autocorrelation of the light and n~r2) is the second factorial moment measured with sample time T. This well known procedure removes all problems associated with correlated afterpulsing and deadtime in the PMT's [28,29]. At the low count rates measured (am q2) negligible distortion is expected from the single bit (by multibit) multiplication carried out in the correlator [ 27 ]. The zero delay time point was accessed using an external delay circuit synchronised 203

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OPTICS COMMUNICATIONS

RESULT 1 TD = 20#s 1.1 g(2) (1") •

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Fig. 2. Normalised correlation function of signal channel counts as a function of delay time r. to the correlator sample time clock. We re-emphasise here that the correlator is not synchronised to detection events in the trigger channel. Two typical experimental results are shown in fig. 2 along with a control result where the crystal and laser were replaced by a simple tungsten filament light source attenuated to similar brightness. In result 1 the shutter-open-width was made as short as possible ( t ~ 150 ns) with some loss in efficiency. This allowed a deadtime of 20/zs and sample time of 19/ts to be used. Antibunching evidenced by a positive zero time slope in the correlation function is clearly seen. As g(2)(0) ( - n (z)) is below 1 the photon statistics are also sub-poissonian. A longer shutter open time (t=0.5 /~s) led to better efficiencies but smaller effects, as in result 2, (ZD=40 /tS, T = 37/~S). Count rates were low ( ( n ) ~ r/2) hence all results were 204

1 M a y 1987

accumulated over long periods (of order 24 hr) by averaging shorter (half hour to one hour) experiments to avoid problems due to long-term laser drift. Detector dark counts (5-10 cps) contributed significantly to the results shown despite cooling the photocathodes to below 3 degrees Celsius. A summary of the results including dark count correction, comparison with theory and estimated Fano factors are shown in table 1. The post detection Fano factors were calculated assuming a single detector could be used (i.e., count rates including dark count were summed) while predetection assumed no beamsplitter and PMT absolute quantum efficiency of 0.020+0.004 [30]. Clearly the reduction of the Fano factors below 1 is statistically significant but not large in magnitude, even predetection. Primarily this degradation is due to the losses in the signal channel amounting to an equivalent transmission coefficient of 0.05. The major causes of this are: limited diffraction efficiency of the acousto-optic switch (transmission around 0.3), fibre losses (transmission including launch and collection optics around 0.5) and alignment losses ( > 0 . 5 ) . Quoted acousto-optic diffraction efficiencies for well collimated beams are greater than 80%. A trade off between switching speed and diffraction efficiency occurs due to the use of the high numerical aperture multimode fibre. A monomode delay fibre optimised for use around 650 nm would allow better collimation, hence diffraction efficiency, as well as possibly reducing fibre losses. Electro-optic switching (with nanosecond switching time) could be used with polarisation preserving monomode fibres. Alignment losses appear to be due primarily to filter band edge absorption and photomultiplier quantum efficiency fall-off at long wavelengths as crystal tilt, hence dispersion, is at present not large enough to ensure that the apertures limit the bandwidth of the detected light. Use of smaller apertures along with more laser power and a more optimal choice of crystal axis tilt could reduce these losses. In principle, the total signal channel loss can be reduced to below 50% [ 25 ] indicating achievable predetection Fano factors below 0.5. The low intensity reported here is primarily limited by laser power and shutter switching speed (versus efficiency). There are at least three orders of magnitude to be gained in intensity before the limits of elec-

Volume 62, number 3

OPTICS COMMUNICATIONS

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trooptic shutter technology are reached. No useful noise reduction will be achieved without higher quantum efficiency detectors. We have already incorporated an experimental [26], high quantum efficiency, avalanche photodiode detector in this apparatus to improve results. Work is at present in progress [31 ] on an actively quenched photon counting APD which can be cooled to reduce the high dark count inherent in these devices when operated at high quantum efficiency. In principle the quantum efficiency of this type of device is only limited by the analogue quantum efficiency of the APD (around 0.85 at 830 nm). In conclusion, we have clearly demonstrated a subpoissonian light source producing up to 1685 photons per second with a Fano factor of 0.985 and normalised second moments down to 0.42. This is comparable with previous sub-poissonian sources [ 11,12] but as mentioned earlier the partial collimation of the source should allow much larger variance reduction in future. As yet the variance reduction is not large enough to be of practical use. Possible improvements to the apparatus, detailed above, could significantly reduce this predetection Fano factor (to below 0.5) with increased source intensity (X 103), and the development of higher quantum efficiency photon counting detection systems is underway. Finally, we note that variants on this apparatus using high quantum efficiency analogue detectors could be used to produce sub-poissonian (but not antibunched) light sources with nanowatt to microwatt powers.

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We would like to acknowledge several useful discussions with E.R. Pike, R.G.W. Brown, J.S. Satchell, K.D. Ridley and J.G. Walker during the course of this work.

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[1 ] D.F. Walls, Nature 306 (1983) 141. [2] H. Paul, Rev. Mod. Phys. 54 (1982) 1061. [3] H.P. Yuen and J.H. Shapiro, IEEE Trans. Inform. Theory IT24 (1978) 657; IT26 (1980) 78. [4] J.H. Shapiro, H.P. Yuen and J.A. Machado Mato, IEEE Trans. Inform. Theory, IT25 (1979) 179. [5] C.M. Caves, Phys. Rev. 23D (1983) 1693. [6] C.K. Hong, S.R. Friberg and L. Mandel, Appl. Optics 24 205

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(1979) 3877. [ 7 ] E. Jakeman and J.G. Rarity, Optics Comm. 59 (1986) 219. [8] C.K. Hong and L. Mandel, Phys. Rev. Lett. 56 (1986) 58. [9] P. Grangier, G. Roger and A. Aspect, Europhys. Lett. 1 (1986) 173. [ 10] H.J. KJmble, M. Dagenais and L. Mandel, Phys. Rev. Lett. 39 (1977) 691. [ 11 ] R. Short and L. Mandel, Phys. Rev. Lett. 51 (1983) 384. [ 12] M.C. Teich and B.E,A. Saleh, J. Opt. Soc. Am. B 2 (1985) 275. [ 13] J.G. Walker and E. Jakeman, Optica Acta 32 (1985) 1303. [14] R.E. Slusher, L.W. Holberg, B. Yurke, J.C. Mertz and J.F. Valley, Phys. Rev. Lett. 55 (1985) 2409. [ 15] B.E.A. Saleh and M.C. Teich, Optics Comm. 52 (1985) 429. [ 16] N. Imoto, H.A. Hans and Y. Yamamoto, Phys. Rev. A 32 (1985) 2287. [17] H.P. Yuen, Phys. Rev. Lett. 56 (1986) 2176. [ 18 ] F. Capasso and M.C. Teich, Phys. Rev. Lett. 57 (1986) 1417. [ 19 ] J.G. Walker and E. Jakeman, SPIE492, ECOOSA'84 (1984) 274. [20] E. Jakeman and J.G. Walker, Optics Comm. 55 (1985) 219.

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[21] S. Machida and Y. Yamamoto, Optics Comm. 57 (1986) 290. [22] J.H. Shapiro, M.C. Teich, B.E.A. Saleh, P. Kumar and G. Saplakoglu, Phys. Rev. Lett. 56 (1986) 1136. [23] E. Jakeman and J. Jefferson, Optica Acta 33 (1986) 557. [24] J.W. Muller, Nucl. Inst. Meth. 117 (1974) 401. [25] R.G.W. Brown, E. Jakeman, E.R. Pike, J.G. Rarity and P. Tapster, Europhys. Lett. 2 (1986) 279. [26] R.G.W. Brown, K.D. Ridley and J.G. Rarity, Appl. Optics 25 (1986) 4122. [27] E. Jakeman, in: Photon correlation and light beating spectroscopy, eds. H.Z. Cummins and E.R. Pike (Plenum NY and London, 1974) p. 75. [28] F.T. Arecchi, M. Corti, V. Degiorgio and S. Donati, Optics Comm. 3 (1971) 284. [29] H.C. Burstyn, R.F. Chang and J.V. Sengers, Phys. Rev. Lett. 44 (1980) 410. [30] J.G. Rarity, K.D. Ridley and P.R. Tapster, Appl. Optics, submitted. [ 31 ] R.G.W. Brown, R. Jones, K.D. Ridley and J.G. Rarity, Appl. Optics, submitted.