Controlling the correlation between the signal and idler mode photons

15 June 1996

OPTICS COMMUNICATIONS ELSEVIER

Optics Communications 127 (1996) 237-242

Controlling the correlation between the signal and idler mode photons K. Kono ‘, M. Koashi, T. Hirano 2, M. Matsuoka 3 Institute forSolid State Physics, University of Tokyo, 7-22-I Roppongi, Minato-ku, Tokyo 106, Japan

Received 29 August 1995; accepted 18 January 1996

Abstract Correlation measurements of the outputs of a nondegenerate optical parametric amplifier with weak coherent input light were performed. By choosing the relative phase between the input and pump light, we observed positive and negative

correlation between the signal and idler photons.

1. Introduction It is well known that the process of parametric down-conversion can be used to generate quantum correlation between photon pairs. The entangled photon pairs exhibit nonclassical intensity interference [ 1] and/or nonlocal correlations [ 21. These features have attracted a great deal of attention and various theoretical and experimental work has been done to explore the nature and possible applications of the entangled photon pairs [ l-101. If we seed input light to the parametric process, not only down-conversion but also upconversion process can take place. In this paper, we study intensity correlation between two output lights from a nondegenerate parametric amplifier with seed light. We show that we can establish negative correlation among photons of the two output lights by set-

’ Present address: National Research Institute for Metals, 1-2-1 Sengen, Tsukuba, Ibaraki, 305, Japan. * Present address: Institute of Physics, University of Tokyo, 3-8-l Komaba, Meguro-ku, Tokyo, 153, Japan. 3 Present address: Department of Physics, Kumamoto University, 2-39-l Kurogami, Kumamoto, 860, Japan.

ting appropriately the phase of the seed light relative to that of the pump light. The quantum mechanical description of the parametric down-conversion is the splitting of a single photon of frequency 2w into two photons of frequency NW. Experimentally, this was first verified by Burnham and Weinberg in 1970 by observing the strong positive correlation between the signal and idler photons 133. The time interval between the signal and idler photons was intensively measured by Mandel et al. [ 4,5], and they showed that it corresponds to the coherence time of the parametric fluorescence (inverse of the spectral width). In the case of up-conversion process, on the other hand, two nearby photons of frequency w are simultaneously annihilated and one photon of frequency 201 is created. If input signal and idler beams have no correlations, i.e., photons are distributed randomly, selective annihilation of coincident paired photons results in the negative correlation among the photons of the beams. The direction of the energy flow between the input light and the pump light is determined by the relative phase. Therefore, we may control the correlation between them by changing the

0030-4018/96/$12.00 Copyright @ 1996 Elsevier Science B.V. All rights reserved. PIISOO30-4018(96)00082-X

238

K. Kono et aI./Optics ~o~~~~~a~o~

relative phase. In our experiment we used pulsed light in order to enhance nonlinear response and to shorten the ‘effective’ response time of coincidence measurement. In Section 2 we introduce the cross-correlation function of pulsed light and its normalization. In Section 3 we describe our experiment and in Section 4 we compare the experimental result with a simple single-mode theory. 2. Cross-corrfdation Using a mode-locked pulsed laser, we measured the cross-correlation between the signal and idler photons by two detectors whose response time is larger than the pulse duration. The observed intensity correlation between nth neighboring pulses is

where 1, and li are the intensity operators for the signal and idler photons respectively. T is the pulse interval. Photo-detections are defined as coincident when they are within the same pulse. Hence, the time integration runs over the duration of a pulse. K is a constant which is related to the detection efficiency. The number of accidental coincidence NaCCcan be written as follows: N,,=K(Sl,(f)dr)(JL(t+nT)dr).

(2)

Using the accidental coincidence counts, the cross correlation function is normalized as follows: (Jr,(r)dtJl,(r+nT)dr) g’2’= (/l,(t)dr)

(/1i(r+nT)dt)’

(3’

The cross-correlation function gi2) between the signal and idler is proportional to the probability of the detection of the signal and idler in the 8th neighboring pulses. Therefore, when the value of gh2’ is larger than unity, the signal and idler photons are more likely to be detected coincidently compared to the random case. In this case the signal and idler photons have positive correlation [3,4]. When the value of gi2) is smaller than unity, the signal and idler photons are less likely

127 (1996) 237-242

to be detected coincidently. In this case, the signal and idler photons have negative correlation. When the value of gi2’ is unity, there is no correlation between the detection of the signal and idler photons.

3. Experimextt The ex~riment~ setup is shown in Fig. 1. A continuous-wave mode-locked Nd3+-doped yttrium aluminum garnet (Nd:YAG) laser (Spectron model ML903) generates infrared (IR, w) pulses at 1064 nm. The pulse duration is 100 ps and its repetition rate is 82 MHz. Second harmonic (SH, 2~) light at 532 nm is generated in a 15mm-long LiBs05 (LBO) crystal and used to pump the single-pass nondegenerate optical parametric amplifier (NOPA). It is made of a Smm-long KTiOPO3 (KTP) crystal which is Type-II phase matched by angle tuning. In this confi~ration the signal and idler photons are in different modes having ~~ndicul~ ~l~i~tion with each other. The residual IR light from SH generation is attenuated (to the order of pW) to seed the parametric amplifier as follows. Two things are important to observe the negative correlation between the signal and idler; stability of the relative phase ((p) between the IR and pump light and the adjustment of the IR light intensity. The collinear configuration as in Fig. 1 stabilizes the relative phase during the measurement. To adjust the IR light intensity without affecting the pump light intensity, a harmonic wave plate (HWP), which acts as a half-wave (1\,/2) plate for the IR light and a full-wave (A> plate for the SH (pump) light, and a polarizer are used as a variable attenuator for the IR light. After the polarizer, another HWP is placed to rotate the polarization vector of the IR light by 45 degrees to seed the signal and idler modes of the NOPA equally. The relative phase between the IR and SH light is changed by moving a wedged BK7 glass plate (GP) which has different indices of refraction for the IR and SH light. The difference in optical path length for the IR and SH light varies with the glass plate thickness. The signal and idler are separated using a polarizing beam splitter (PBS). In order to minimize detection of spurious fluorescence, which has different frequency or k vector from those of the input IR light, an etalon and an interference filter (IF) are placed after the NOPA. Photon counting

K. Kono et al. /Optics Communications 127 (1996) 237-242

239

start

T.4C Fig. I. Experimental apparatus. nondegenerate optical parametric photodiodes.

HWP: harmonic wave plates, Ml-2: mirrors, GP: wedged glass plate (BK7), P: polarizer, NOPA: amplifier (KTP), ET: etalon, IF: interference filter, PBS: polarizing beam splitter, APDl-2: avalanche

160

I

140

120

40

20

-12

0

12

36

24

Delay

Fig. 2. Typical positive correlation between the signal and idler. This experiment measured fluorescence. The NOPA is pumped by the SH light whose intensity is 50 mW. g,$*’ is 18.3.

is performed with two silicon avalanche photodiodes ( APD, RCA model SPCM-lOO-PQ, quantum efficiency is 0.8%@1060 nm, and dead time is 200 ns both specified by manufacturer) and their outputs are fed to the start and stop inputs of the time-toamplitude converter (TAC) which measures the time intervals between the signal and idler photons. The output of the TAC is processed by an A/D converter, a multi-channel analyzer (MCA) and a computer. The total detection efficiency for a start or stop channel is estimated to be 5 x 1O-4 using the measured optical losses and the quantum efficiency of 0.8%. This ex-

46

60

(ns) the correlation

function

of the parametric

perimental setup is similar to the one we used for the observation of photon antibunching [ 111. The major differences are as follows. First, a nondegenerate parametric amplifier is used instead of a degenerate parametric amplifier. Secondly, the signal and idler photons are separated by a polarizing beam splitter (PBS) and cross-correlation is measured. In the previous experiment auto-correlation was measured. The number of accidental coincidence Nacc is calculated from the measured counts using the following relationship,

240

K. Kono et al./Optics

Communications 127 (1996) 237-242

20

40

60

Delay (ns) Fig. 3. Typical

Nx,

negative

= NI M-IT,,

7

correlation

between

the signal and idler. The NOPA is pumped by the SH light whose intensity

(4)

where Nr is the number of total valid start of the TAC. N2 is the number of total stop of the TAC. T,,, corresponds to the total measurement time and T corresponds to the pulse intervals. If the start and stop signal arrive within the time interval of T, they are regarded to be simultaneous. Fig. 2 shows the correlation between the signal and idler of the parametric fluorescence in which no IR light is seeded. The pump intensity for the NOPA was 50 mW. The counting was accumulated for 10000 seconds. The shapes of the peaks in Fig. 2 (and similarly in Fig. 3) do not reflect the actual pulse duration but the APD response time. The peak at n = 0 has 1955 coincidence counts which is 18.3 times larger than the accidental coincidence rate after correction for the dark counts. This shows there is the strong positive correlation between the signal and idler photons. A typical result of the negative correlation between the signal and idler is shown in Fig. 3. In this experiment, the pump intensity for NOPA was 650 mW and the relative phase is chosen for the maximum deampli-

is 650 mW.

fication of the IR light. The counting was accumulated for 4000 seconds. In this experiment the coincidence counts for the time delay n = 0 is 3095 and the accidental coincidence counts is 4607. Considering the effect of the dark count of 800 per second, the value of gi2) is calculated to be 0.61 f 0.02. Fig. 4 shows the experimental values of &’ between the signal and idler photons. When the relative phase is chosen for the amplification of the IR light, the correlation is always positive. On the other hand, when the relative phase is chosen for deamplification, the correlation becomes either positive or negative depending on the input intensity of the IR light. In this measurement the NOPA is pumped by the SH light whose intensity was 500 mW.

4. Discussion We would like to with a single-mode predicts positive and signal and idler. In

compare the experimental result theory. The single-mode theory negative correlations between the this theory the signal and idler

K. Kono et al. / OpticsCommunications127 (19%) 237-242

241

states with equal intensity Icy{*.The cross-correlation function between the signal and idler photons of the NOPA is as follows:

=l-f-

cash 2rcos co)+ sinh* 2r

41a12sinh 2r(sinh2r4[ jal*(cosh2r-

sinh2rcosq)+sinh*

r]*

’ (6)

mJ = 1aI e-‘“*,

0

I

0.0

0.5

I

1

1.0

1.5

input signat

I

I

I

2.0

2.5

3.0

(idler) intensity (photons/pulse)

Fig. 4. Experimental results of gi*) are plotted along with the single mode theory for various input signal (idler) light intensity The upper line corresponds to the case of m~imum ~pli~cation 9 = v. The lower line corresponds to the case of maximum deamplification 9 - 0. Classical parametric gain parameter r is 0.104 which is calculated by equating n(9 = ~r)/n((p = 0) with exp(4r). The measured gA*’for maximum amplification is plotted is plotted with with box and g:” for m~imum d~plification circfe.

modes are treated as distinct single modes and the depletion of the pump light is neglected. The creation operators of the output signal and idler modes (bi, 6; ) of the NOPA are expressed using the input signal and idler operators (a,, CZ~, ui, ai) as follows: bf = CZ+ s cash r - ai e’@sinh r , btI = atI cash r - a, e’+ sinh r 1

(5)

where r is a squeezing parameter, 4 is the phase of the pump light. We assume that the input signal and idler modes incident upon the NOPA are in coherent

ffj

=

{CfI

ewiei,

Cp= 4 - f3$- @i,

where cpcorresponds to the relative phase between the IR and pump light. When the relative phase ((p) is 0, the maximum deamplification of the IR light takes place. When the relative phase ((p) is chosen to be T, the m~imum ~plification takes place. The second term of gh2)originates from the commutation relations between b, and bj, or bi and bit. This term leads to negative correlation (g$“’ < 1) , or positive correlation (gi2” > 1). When IcyI--+ 03 the effect of this term disappears. Positive correlation has been experimentally confirmed as twin beams. The negative correlation which is described in this paper is the cross-co~elation between the nondegenerate beams. Therefore, it is different from the negative correlation of the degenerate signal and idler beams, i.e., the correlation of the ~tibunchi~g. Rq. (6) is used to calculate the theoretical value, and it is shown in Fig. 4. In order to determine the classical parametric gain parameter r, we compared the photon counting rate for the m~imum amplification ntul = 71) (counts/s~) and that for the m~imum deamplification n(q~ = 0) of the signal output. The gain parameter r is determined to be 0.104 by equating the ratio n(p = ~)/n( Q = 0) with exp(4r). We calculated the number of photons per pulse by using the total detection efficiency, and used it as the input intensity jcrl*. Fig. 4 shows that the single-mode theory explains the behavior of gf’ at least qu~itatively. The behavior may be understood as follows. When the maximum amplification takes place, the correlation is always positive reflecting the fact that the signal and idler photons are always created simultan~usly. When the maximum deamplification takes place, the correlation has the minimum value at jnj2 N r. It is

242

K. Kono et al./Optics Cornrn~~c~tion~127 (1996) 237-242

less than one. This negative correlation is a result of annihilation of paired photons. When the IR light input is very weak, the cross-correlation is always positive regardless of the relative phase. In this region, the parametric fluorescence is dominant and the signal and idler have the positive correlation. When the IR seed light is very strong, the correlation is neither negative or positive. 5. Conclusion

We have observed both positive and negative correlation between the signal and idler photons. The crosscorrelation is controlled by the relative phase between the input IR light and the pump light. When the relative phase is chosen for the maximum amplification, the cross-correlation is always positive resulting from the fact that the signal and idler photons are always created in pair (twin photons). When the m~imum deamplification is achieved, the cross-co~elation showed either positive or negative depending on the input IR intensity of the NOPA. We compared the experimen-

tal result with the single-mode theory. The negative correlation as well as positive one is due to the effect of the quantum mechanical commutation relation between operators.

[ 11 R. Ghosh and L. Mandel. Phys. Rev. Len. 59 ( 1987) 1903. [2] P.R. Tapster, J.G. Rarity and PC.M. Owens, Phys. Rev. I_& 73 (1994) 1923. [3] D. Bumham and D. Weinberg, Phys. Rev. I.&t. 2.5 ( 1970) 84. [4] S. Friberg, C. Hong and L. Mandel, Phys. Rev. Lea. 54 (1985) 2011. [5] C.K. Hong, Z.Y. Ou and L. Maudel, Phys. Rev. J_ett. 59 (1987) 2044. [6] A. Heidmann, R. Horowitz, S. Reynaud, E. Giacobino, C. Fabre and G. Gamy, Phys. Rev. Len. 59 (1987) 2.555. [7] P. Kumar, 0. Aytiir and J. Huang, Phys. Rev. L.ett.64 ( 1990) 101s. 181 Y.H. Shih and C.O. Alley, Phys. Rev. Len. 61 (1988) 2921. [9] Z.Y. OK and L. Mandel, Phys. Rev. I_&. 61 (1988) 50. [lo] Z.Y. Ou, S.E Per&a and H.J. Kimble, Appl. Phys. B 55 (1992) 265. [ 111 M. Koashi, K. Kono, T. Hirano and M. Matsuoka, Phys. Rev. Lett. 71 (1993) 1164