Simultaneous entanglement in spin and space-time of a two-photon quantum state generated in type-2 spontaneous parametric down-conversion is demonstrated by the observation of quantum interference with 98% visibility in a simple beam-splitter (Hanburry Brown-Twiss) anticorrelation experiment. The nonlocal cancellation of two-photon probability amplitudes as a result of this double entanglement allows us to demonstrate two different types of Bell's inequality violations in one experimental setup

Pittman, T. B.

Rubin, M. H.

Sergienko, A. V.

Shih, Y. H.

English

NASA Technical Reports Server

_" /i J
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Two-Photon Entanglement and EPR Experiments Using Type-II
Spontaneous Parametric Down Conversion
A.V. Sergienko, Y.H. Shih, T.B. Pittman, and M.H. Rubin
Department of Physics, University of Maryland Baltimore County
Baltimore, MD 21228 USA
Abstract
Simultaneous entanglement in spin and space-time of a two-photon quantum state generated in
type-II spontaneous parametric down-conversion is demonstrated by the observation of quantum in-
terference with 98 % visibility in a simple beam-splitter (Hanburry Brown-Twiss) antieorrelation ex-
periment. The nonloeal cancellation of two-photon probability amplitudes a_s a result of this double
entanglement allows us to demonstrate two different types of Bell's inequality violations in one exper-
imental setup.
1 Introduction
Two-particle entangled states play a particularly important role in the study of the Einstein-Podolsky-
Rosen (EPR) paradox [1] and in the test of Bell's inequalities [2]. Entangled states are states of two or
more particles that can not be written as products of single particle states. [1]. The physical consequences
resulting from the EPR states violate cl,'ussieal local realism [3].
In the past, EPR type two-particle entanglement hms been demonstrated by two types of experiments:
(1) two-particle pol_ization correlation measurements; most of the historical EPR-Bohm experiments [4]
and the memsurements testing Bell's inequality exhibited nonlocal two-particle polarization correlation
[5]. These experiments demonstrated the EPR type two-particle spin-type entanglement. (2) two-particle
interference (fourth order interference) experiments; recent two-particle nonclassical interference experi-
ments demonstrated two-particle space-time entanglement [6].
Usually two-photon entanglement appears in the form that if one wants to measure the linear po-
larization of a single photon, one would find that neither of them ha,s a preferred polarization direction,
however, whenever a single photon is measured to be polarized in a certain direction the other one must
be polarized orthogonal to that direction. A typical EPR type two-photon space-time entangled state,
was proposed by Franson recently [7]. In this state one can never predict "which path" for a single photon,
however, if one of the photons traveled through the longer (shorter) path the other must have traveled
through the longer (shorter) path. The signature of this state is a cosine sum frequency interference
fringe pattern of the coincidence counting rate.
The non-local spin or space-time two-particle entanglement phenomena is unusual from the classical
theory point of view. The third type of simultaneous two- particle entanglement both in spin and in space-
time will be discussed in detail by reporting several experiments. In these experiments, it is interesting to
see that the measurement of the spin and space-time observables of either particle determines the value
of these observables for the other particle with unit probability.
2 EPR experiments
Spontaneous parametric down-conversion (SPDC) is one of the most effective sources for generating two-
photon entangled states. In SPDC a pump beam is incident on a birefringent crystal. The nonlinearity of
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the crystal leads to the spontaneous emission of a pair of entangled light quanta which satisfy the pha_sc
matching condition [8],
where w; is the frequency and f_i the wave vector, linking pump (p), signal (1), and idler (2). The
down-conversion is called type-I or type-II depending on whether the photons in the pair have parallel
or orthogonal polarization. The light quanta of the pair that emerges from the nonlinear crystal may
propagate in different directions or may propagate collinearly. The frequency and propagation directions
are determined by the orientation of the nonlinear crystal and the phase matching relations in (1).
In order to understand the two-photon behavior of SPDC, consider the experiment which is shown
in Fig. 1, a simple beam-splitting experiment. Assume that a type-II BBO (fl - BaB204) crystal is
used for the SPDC. The collinear down-conversion beam is split by a beamsplitter. The beamsplitter
is mssumed to be pol_ization dependent so that the o-ray is transmitted and the e-ray is reflected.
Single photon counting detectors D1 and D2 are placed in the transmission and reflection output ports
of the beamsplitter for detecting the o-ray and the e-ray, respectively. An introduction of the effective
wavefunction _(tl, t2) is helpfill for understanding the physics of the phenomenon.
? | =t,= <:_
702.2 am l BBO
..,__.__ Type II I
_-_, c,yst= ,',.ri..,, •
Plates \ I
'._/_=yz_o) I Figure 1. Schematic experiment for
" t study of the type II SPDC biphoton.
i s_ .__.I _'_'" I
I -I c.,.,.t,,, BS is a beamsplitter. Dt and D2 are
_] N¢___ photon counting detectors. A coinci-
_._ (4s>i_ dence circuit is used for recording theI \l\l coincidence rate.
For collinear type-II SPDC, a two-photon part of the state exiting the crystal may be ealctflated from
the standard theory of SPDC [9].
I,r) = E ,+(_v,+ _2 - ,v,,)¢Ck,+ k2- kp),,ot (_, (k,)),,.t (_v2(k2))o> (2)
1,2
The effective waveflmction may be calculated for the system presented in Fig.1 [9]
+(tl,tm) = (OIEI+)E(2+)I+). (3)
• (tt, t2) = v(q + t2)u(q - t2) (4)
v(t) = voezpC-i_pt/2)
Vu(t) = uOezp(--iwdt/2) dr[1 - exp(-uDL)]/(iuDL)exp(-ivt)
= e.r,p(-iwet/2)II(t)
160
"_to DL >t >0I](t) = 0 (5>
where "0, '**.f_;trc constants (norm;dizat.i,m). Wc lmv_ nt)pr,-_ximat.e_t t.lw tromp t.o be a piano wave iI, t.he
cah'uladon. If l:he pump tn'nnl were taken t.o 1.: a Gmtssian with }.mdwidth czp, it is n,,t difficult t:o show
t.hat, the const;u_t v() will be replaced by ;t Gaussian function voc:?:p(-cr_t2/8).
E(luatioll (.1)demonstrates a t.wo dimensional wavepacket, referred t(J ;m the t.w,>t)hot,m effective
w;weflmCdOll ,u' fin" short tile Biphohm. [8, 9]. It is clear that the biph,_ton is entangled in spaco-time
l)(?cnusc the wav_?funct:ion can not: f;wt(n' int.o a f, mction (,ftt _im,-.s a timer.ion ,d t2.
Fig. 1 illustm'tes the ,'.xt)c_rim,'nt_d set. up fin the vm'ificadon ,,f II-shaped lfip},,t.,m. The tmamst,litter
is t_,Jnrizat:.i_,n incbpendcnt, so thin. }_,Ml tim o-r;w and the c-ray ('(told be transmitt.,.d (n" r(.fle('tod to
t.rigg,.r D1 or D._,. A Glan Th(..ps, m li.m_r t)ol;u'iz_tti(ul mmlyzer, m'iented at 45" rclat.iv,, l,, the o-ray
and c-r;ty l)olariznt.ion pl_mrs ,_f dm BB() crystal, is place_l in fl,mt of each of the (tetectors. Birefl'ingent
ntat,wial, fl)r ('×mnt>le a set ()f quartz plat.cs, is introduced into tho single incid,mt. }),!am for mmfip,flndng
tlw ,,ptical d,Jay 5 belwe,'n the o-ray and lJle ¢>ray. The fast axes ,d the (lll;t_l'tZ plat.s were carcflflly
aligned to lnatc}, the o-r;ff (_l" c-lmy in_la.rizati,m planes ,)f the BB() crystal. In ,n'(h_r t.,, se_ l.h,, '..tu,'al
._pcctr'..l sh.op. ,_f _.t_e SPDC. n- ;tlly narrow|)mM spcct:ral tiltcl'S a.r,. ,me(1 except UV tilt. (_tI' tilters t,, get
rid .f t,h(! t)UlUt_ s('at, t,(!r(:d ligl,t [[()].
It. is int.cr,'st.in g to see Chn¢ wlwn ,_,_ quartz plm:cs ;u'e used the two terms iil the {>f['octivc w;_v.*',m('ti.n
(4) do _.,t. sI.,w any intcrf.r.twc sil,c{ _ [I(tl - re) arm II(t., - tl ) ,h, _,,t. owM;,p. Physically it. means that
tit,', o-r;ty ;tn(t t.lw (-rtty ph_t(ms ;tl'(? w,'ll disth_guished in spac(,-tinle. Now c, msidcr tlt,> case ,}t"having a
(t_l;trt.z tJnt.c in the down-('_nv,_rsi_._ incident beam. [f we ;dign t.he qum't.z ca.reflllly to lnatc}_ its f;tst, axis
t.,, tim o-ray tndm'izati_,n ,lir,'cti_,n ,,f t.lw I_B(). mt opt.ical delay, £ _ (n,, - 'n,.)l/(:, is introd,u:,!,l betw,'el_
the o-fay gtIl(] LIt," c-t';ty (d' BB(). wl.'r,_ n,, an,t ._ are d.'. in(h'x of rc]'racl.ion of the (lU;U't% t)l;tt,_s fl,r
/.he o-ray a.n(t tll(. C-ray ,,f 13B(), a,l.i 1 is the thickness of the ([ll;t.l'tZ [)I&U< Tilt-.. (qft_ctiv(! w;tv(_fullc'tion
I.I_?C,_III,_S ("(,llSi,t"]' t:h,? ;ul.:tIyzcl',S ;i.1_! sl!t. ;tl; 45"),
9(_.t-,) = ,r,,_.,,,,(t_ + t,, - _)[v,(t_ - t2 + _) -,,(-t_ + te +,_)] ((;)
It is ,_nsy t.,, s('(', fr, ml etl.(6) dmt th,u'c is interfl'.rence now, because th,_ tw,) t.ern,s _mu'la.l). \_hen
= I)L/2 ,the two) terms c,,mt)h_tcly (m!rht t) a.nd dmrefl_re c:anc(!l e;tch other. This tn;ty }),! (',msi(t,_r,'d ns
a tmrfl'ct. ;u_ti-c(_rrelad_m.
I_,. = lt,.[1- p(_)]
0 -_c, < _ < 0
,,_ 0 < ?_ < DL/2
/' = 1-_:(_-DI/2) DL/2 < ,S < DL
{} DL < 5 < _c,
(7)
The width and the shat)e ,_f the l,iphot,m can be evaluated by t.}_,: width and the shape of R,..
Fig.2 reports typically ,)bs,..rw:d "V-shape" c(,inciden('c rat,', llle;/.Sllrelllellt;.s ;_s ;t flm(:t.ion (,f the .ptical
dcl;w ,5. which verifies the [I-sh;t[)(_ ,_ffectiw_ w;tvefllll(:tioll [10]. E;tch of the d_tt.;t points ('()rr(_stmtl(lS to
diff'or(mt nmnbors of qunr_z I)lat(>s r,'maining in the path of the down-c(,nversi,,n in('i,hmt )>cam. It. is
easy t() find dmt. the vert(,x ()f tim V-s}mp(" flmction has a displac(,.nmnt ()f (72 :t: 3)./'s from Zel'(), which
161
corresponds to a time delay of DL/2 in a (0.56 + 0.05)ram BBO crystal.
o 120o - z = = . _; _ooo=t - *_l tt
m
,OOo 2500 o(_
a_
400 1000
_2 200 $00
-6
0
" ' ' _ • J • 0
"300 "240 -180 -12(] "60 0 60 t 20 180 240 300
Optical Delay 8 (fsec)
A strong correlation which appears in the form of almost a 100% destructive quantum interference
is a clear demonstration of the situation where the Einstein-Podolsky-Rosen argument [1] is directly
applicable. The triangular shape of the correlation flmction is a clear signature of the rectangular shape
of original two-photon effective wavefunction. The discussion of the effective waveflmction is important
Mso for the understanding of the two-photon double entanglement.
Figure 2. Lower curve: Coincidence
counts ,as a flmetion of optical delay,
which corresponds to a certain number
of quartz plates. The solid curve is a
fitting curve of eq.(7). Upper curve:
Single detector counts.
3 Double Bell's inequality
Taking advantage of the spin and space-time entanglement of the biphoton, another type of two-photon
interference phenomena can be demonstrated. With the addition of a Pockel's cells, and a re-orientation
of the quartz plates and polarizers, the coincidence counting rate exhibits interference modulation of
the pump frequency when manipulating the voltage across the Pockel's cell, regardless of the optical
delay by the quartz plates (which is rn,nch greater than the, coherence length of the signal and idler down-
conversion fields). This two-photon interference effect is again due to a noncl,assical two-photon state
which is entangled both in spin and in space-time.
Type-II D2 F__,.II I Bao
2.4mm 11 quartz plates BS
quartz
Figure 3. Schematic set up for the new type two-photon interferometer.
F1
P1 A1
The schematic set up of the experiment is illustrated in Fig.3. The type-II SPDC is the same ,as that
in the quantum beats experiment. The collinear down-conversion beam p`asses through a set of crystal
quartz plates before the beamsplitter. The first three quartz plates, which sum to 2.4ram in thickness, are
oriented in a way to make the two terms of the H-shape function completely overlap (see the discussion
in section 2). 11 more crystM quartz plates follow these three. The fast axes of these 11 quartz plates are
aligned carefillly to be oriented at 45 ° relative to the o- ray and the e-ray polarization planes of the BBO
in order to introduce a new b`asis associated with the fast and slow axecies. Each of these quartz plates
is (1 4- 0.1)ram in thickness, resulting in an optical delay Al _ 9#m between the f_t and the slow rays
162
of the quartz crystal at wavelengths around 700 nm. The optical delay is about 99#m after 11 quartz
plates in comparison with the coherence length of the field which is about 25#m. Therefore, the IX} and
the )Y) components of the original o-ray and e-ray of suffer enough opticM delay to be non-overlapping,
where IX) and mY) correspond to the fast and the slow axes of the quartz plates. A Pockel's cell with
fa.st and slow axes carefiflly aligned to match the IX) and the mY) axes is placed after the quartz plates
in each output port of the beamsplitter for fine control of the optical delay between the IX} and the [Y).
The spectral filters .fl and .fu have Gaussian shape transmission functions centered at 702.2nm, with
bandwidths of 19nm(filll width at half maximum).
The down-conversion [o) and le} polarized photons both have certain probabilities to be in the IX)
or the [Y) state when pressing through the crystal quartz plates and the Pockel's cells. The optical
delay between the IX} and the IY) is then introduced by the anisotropic refractive index of the quartz
plates and the Pockel's cells. The coincidence time window in this experiment is 1.Snsec, which is much
shorter than the distance between the PockeFs cells. Bell inequality memsurements can be performed for
both space-time variables and for spin variables in one experiment. For the 45 ° oriented polarizers, the
coincidence co, rating rate is predicted to be,
= R 0{1 - 21cos(a at, + n al2)/c} (8)
where Ali/c is the optical delay introduced by the ith Pockel's cell (to simplify the calculation, we assumed
the optical delays introduced by the Pockel's cells are the same).
d
o
G_
F)
Q.
0
o
o
o
o
o
4000
3200 • • • • • • • • • • • • • • • • •
2400 L/
160O
800
0 I , ,
"200 -1 O0 0 1 O0
1000
8O0
600
o
400 0
0
0200
rn
.... 0
200
Change in optical delays cA1 and cA2 (nm)
Figure 4. A typical observed sum
frequency modulation when the cross
voltages of the two PockePs cells are
manipulated (negative values corre-
spond to negative voltages). The in-
terference visibility is (88.2 -t- 1.2)%,
which violates a Bell inequality for
space-time variables by more than 14
standard deviations. [11, 12]
The manipulation of Alp is realized by changing the applied voltage of the Pockel's cells. The
coincidence co,rots are direct measurements, with no "accidentM" subtractions. It, is clear that the
modulation period corresponds to the pump wavelength, i.e., 351.1nm. Contrary to the coincidence
counting rate, the single detector counting rate remains constant when AIp is manipulated, ms is reported
in the upper part of Fig. 4.
It is interesting to see that in the same experiment, a test of a spin variable Bell ineq,,Mity can be
rome by manipulating the orientation of the polarizers at a totally constructive or destructive space-time
interference point. Because of the symmetries present in the measurement, we are able to study one
simple form of Bell's inequalities for polarization variables [13],
= l[R¢(_/8) - R_(37r/8)]/R0] <_ 1/4 (9)
and the mea._ured result is _ = 0.309+0.009, implying a violation of more than 6 standard deviations.[12]
4 Conclusion
Experiments starting with type-II down-conversion arc a very effective mechanism for generating two-
photon entangled states (biphoton). The typc-II SPDC biphoton is entangled both in space-time and
163
spin. A two-photon eff0,ctive wave function produced by Type-II spontaneous parametric down conversion
is studied fin" its natural shape in space-time. The double entanglement of the two-photon state makes it
possible t,) perform EPl:l. type two-photon interference experinlents in a simple beam-st)litting set ,t t) and
test Bell:s inequalities fl)r space-time variables and spin variables in the same experiment. Two-photon
interfi_rence visibilit:y as high as (98 + 2)% has been observed. Experimental tests f,)r the space,-time
variat_les aim spin variables Bell in,xlualities have been measured with violations of 14 and 6 standard
deviations, respectively, in ()he, experim(',ntal set. up.
5 Acknowledgement
This work was supported by the Office of Nawd Research grant no. N00014-91-J-1430.
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Two-Photon Entanglement and EPR Experiments Using Type-2 Spontaneous Parametric Down Conversion

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