Observation of Dark State Polariton Collapses and Revivals

Article (PDF Available)inPhysical Review Letters 96(3):033601 · February 2006with15 Reads
DOI: 10.1103/PhysRevLett.96.033601 · Source: PubMed
Abstract
By time-dependent variation of a control field, both coherent and single-photon states of light are stored in, and retrieved from, a cold atomic gas. The efficiency of retrieval is studied as a function of the storage time in an applied magnetic field. A series of collapses and revivals is observed, in very good agreement with theoretical predictions. The observations are interpreted in terms of the time evolution of the collective excitation of atomic spin wave and light wave, known as the dark-state polariton.
Observation of Dark State Polariton Collapses and Revivals
D. N. Matsukevich, T. Chanelie
`
re, S. D. Jenkins, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich
School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA
(Received 31 August 2005; published 23 January 2006)
By time-dependent variation of a control field, both coherent and single-photon states of light are stored
in, and retrieved from, a cold atomic gas. The efficiency of retrieval is studied as a function of the storage
time in an applied magnetic field. A series of collapses and revivals is observed, in very good agreement
with theoretical predictions. The observations are interpreted in terms of the time evolution of the
collective excitation of atomic spin wave and light wave, known as the dark-state polariton.
DOI: 10.1103/PhysRevLett.96.033601 PACS numbers: 42.50.Dv, 03.65.Ud, 03.67.Mn
Atomic ensembles show significant promise as quantum
memory elements in a quantum network [1–5]. A ‘dark-
state polariton’ is a bosoniclike collective excitation of a
signal light field and an atomic spin wave [6], whose
relative amplitude is governed by a control laser field. In
the context of quantum memories, the dark-state polariton
should enable adiabatic transfer of single quanta between
an atomic ensemble and the light field. Seminal ‘stopped-
light’ experiments that used laser light excitation [79]
can be understood in terms of the dark-state polariton
concept. In a recent work the storage and retrieval of single
photons using an atomic ensemble based quantum memory
was reported, and the storage time was conjectured to be
limited by inhomogeneous broadening in a residual mag-
netic field [10].
We have recently predicted that dark-state polaritons
will undergo collapses and revivals in a uniform dc mag-
netic field [11]. During storage, the dark-state polariton
consists entirely of the collective spin wave excitation.
According to the dark-state polariton concept, the retrieved
signal field should exhibit the collapse and revivals expe-
rienced by the spin wave. The revivals occur at integer
multiples of one-half the Larmor period, with dynamics
that are sensitive to the relative orientation of the magnetic
field and the light wave vector. The spin wave part of the
dark-state polariton involves a particular superposition of
atomic hyperfine coherences [see Eq. (1) below], inti-
mately related to the phenomenon of electromagnetically
induced transparency (EIT) [12,13]. Revivals of single
atom coherences were observed in atom interferometry
[14,15]. Coupled exciton-polariton oscillations in semi-
conductor microcavities have also been reported [16,17].
The remarkable protocol of Duan, Lukin, Cirac, and
Zoller (DLCZ) provides a measurement-based scheme
for the creation of atomic spin excitations [3]. In systems
where EIT is operative, these excitations will, in general,
contain a dark-state polariton component. The orthogonal
contribution may be regarded as a bright-state polariton in
that it couples dissipatively to the excited atomic level in
the presence of the control field [18]. Observation of the
retrieved signal field, however, picks out the dark-state
polariton part, while the orthogonal component is con-
verted into spontaneous emission [11]. A number of pre-
vious works reported generation and subsequent retrieval
of DLCZ collective excitations [1927]. Several of these
studies investigated the decoherence of these excitations in
cold atomic samples [19,23,24,26,27]. It has been similarly
conjectured in these works that the decay of the coherence
was due to spin precession in the ambient magnetic field.
While the observed decoherence times are consistent with
the residual magnetic fields believed to be present, the
observation of collapses and revivals predicted in
Ref. [11] would demonstrate that Larmor precession is,
indeed, a limitation on the quantum memory lifetime.
Moreover, controlled revivals could provide a valuable
tool for quantum network architectures that involve col-
lective atomic memories [35].
We report in this Letter observations of collapses and
revivals of dark-state polaritons in agreement with the
theoretical predictions [11]. In our experiment, we employ
two different sources for the signal field, a coherent laser
output and a conditional source of single photons [3]. The
latter is achieved by using a cold atomic cloud of
85
Rb at
site A in the off-axis geometry pioneered by Harris and co-
workers [25]. Another cold atomic cloud of
85
Rb at site B
serves as the atomic quantum memory element, as shown
in Fig. 1. Sites A and B are physically located in adjacent
laboratories connected by a 100 m long single-mode opti-
cal fiber. The fiber channel directs the signal field to the
optically thick atomic ensemble prepared in level jbi. The
inset of Fig. 1 indicates schematically the structure of the
three atomic levels involved, jai; jbi, and jci, where
fjai; jbig correspond to the 5S
1=2
, F
a
3, F
b
2 levels
of
85
Rb, and jci represents the 5P
1=2
, F
c
3 level asso-
ciated with the D
1
line at 795 nm. The signal field is
resonant with the jbi$jci transition and the control field
with the jai$jci transition.
When the signal field enters the atomic ensemble at site
B, its group velocity is strongly modified by the control
field. By switching off the control field within about 20 ns,
the coupled excitation is converted into a spin wave exci-
tation with a dominant dark-state polariton component;
i.e., the signal field is ‘stored’ [69]. An important con-
dition to achieve this storage is a sufficiently large optical
PRL 96, 033601 (2006)
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thickness of the atomic sample, which enables strong
spatial compression of the incident signal field [5]. In our
experiment the measured optical thickness d 8. The
subsequent evolution of a dark-state polariton in an exter-
nal magnetic field is predicted to reveal a series of collap-
ses and revivals whose structure is sensitive to the
magnitude and orientation of the field relative to the
signal wave vector [11].
As we deal with an unpolarized atomic ensemble, we
must take into account the Zeeman degeneracy of the
atomic levels. Choosing the same circular polarizations
for both the signal and the control fields allows us to retain
transparency [10]. For a
polarized signal field, the
dark-state polariton annihilation operator for wave number
q is given by [11]
^
q; t
t
^
a
k;

Np
p
g
P
m
R
m
^
S
bm
am
q; t

jtj
2
Npjgj
2
P
m
jR
m
j
2
r
; (1)
where t is the control field Rabi frequency, g is the
coupling coefficient for the signal transition, m is the
magnetic quantum number, R
m
C
F
b
1F
c
m1m1
=C
F
a
1F
c
m1m1
is a
ratio of Clebsch-Gordan coefficients, N is the number
of atoms, p 1=2F
b
1,
^
a
k;
is the field annihi-
lation operator for the mode of wave vector k q
!
0
=c and positive helicity, !
0
is the Bohr frequency of
the jbi$jci transition, S
bm
am
q;t1=

Np
p
P
^
bm;am
t
expiqz
t z
=c is a collective spin wave op-
erator, where ^
bm;am
0jb; mi
ha; mj is a hyperfine co-
herence operator for atom 1; ...;N, z
is the position
of atom , and is the hyperfine splitting of the ground
state. When R
m
is finite for all m, the atomic configuration
supports EIT, but when one or more R
m
is infinite, there is
an unconnected lambda configuration, EIT is not possible
and dark-state polaritons do not exist. Specifically, the
excited state jc; m 1i is not coupled by the control field
to a state in the ground level jai. An atom in the state jb; mi
would absorb the signal field as if no control field were
present.
The signal is stored in the form of spin wave excitations
associated with the dark-state polaritons
P
m
R
m
^
S
bm
am
q
for some range of q. During the storage phase, and in the
presence of the magnetic field B, the atomic hyperfine
coherences rotate according to the transformation
^
S
bm
am
q; t
X
F
b
m
1
F
b
X
F
a
m
2
F
a
D
by
m
1
m
tD
a
m;m
2
t
^
S
bm
1
am
2
q; 0;
(2)
where D
s
m;m
0
ths; mjexpig
s
^
Ftjs; m
0
i is the ro-
tation matrix element for hyperfine level s,
^
F is the total
angular momentum operator,
B
B=@,
B
is the Bohr
magneton, g
a
and g
b
are the Lande
´
g factors for levels jai
and jbi of
85
Rb and, ignoring the nuclear magnetic mo-
ment, g
a
g
b
. This rotation dynamically changes the
dark-state polariton population during storage.
The measured signal retrieved after a given storage time
T
s
is determined by the remaining dark-state polariton
population. Stated differently, only the linear combination
of hyperfine coherences
P
m
R
m
^
S
bm
am
q; T
s
contributes to
the retrieved signal. We calculate the number of dark-state
polariton excitations as a function of T
s
using Eqs. (1) and
(2), h
^
NT
s
i
P
q
h
^
y
q; T
s
^
q; T
s
i, and find
h
^
NT
s
i
h
^
N0i
X
m
1
m
2
R
m
1
R
m
2
P
m
jR
m
j
2
D
by
m
2
m
1
T
s
D
a
m
1
m
2
T
s
2
: (3)
In Figs. 2(f)2(j), we show the theoretical retrieval
efficiency for various orientations of a magnetic field of
magnitude 0.47 G, corresponding to the Larmor period of
4:6 s. With the approximation g
a
g
b
it is clear that
the system undergoes a revival to the initial state after one
Larmor period (2=jg
b
j), and thus the signal retrieval
efficiency equals the zero storage time value. Depending
on the orientation of the magnetic field, a partial revival at
half the Larmor period is also observed. For a magnetic
FIG. 1 (color online). A schematic diagram illustrates our
experimental setup. A signal field from either a laser or a
DLCZ source of conditional single photons at site A is carried
by a single-mode fiber to an atomic ensemble at site B, where it
is resonant on the jbi$jci transition. The signal field is stored,
for a duration T
s
, and subsequently retrieved by time-dependent
variation of a control field resonant between levels jai and jci.
All the light fields responsible for trapping and cooling, as well
as the quadrupole magnetic field in the MOT, are shut off during
the period of the storage and retrieval process. An externally
applied magnetic field created by three pairs of Helmholtz coils
(not shown) makes an angle with the signal field wave vector.
The inset shows the structure and the initial populations of
atomic levels involved. The signal field is measured by detectors
D2 and D3, while detector D1 is used in the conditional
preparation of single-photon states of the signal field at site A.
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033601-2
field oriented along the z axis [Fig. 2(f)], the polariton
dynamics is relatively simple. Each hyperfine coherence
^
S
bm
am
merely picks up a phase factor that oscillates at fre-
quency 2mjg
b
j, thus returning the system to its initial
state at half the Larmor period. In this case, the partial
revival is actually a full revival. On the other hand, for
=2 [Fig. 2(j)], a rotation through half the Larmor period
causes the coherence transformation
^
S
bm
am
!
^
S
bm
am
, and,
as a result, the retrieval efficiency is reduced to
P
m
R
m
R
m
=
P
m
R
2
m
2
. The substructure within a half
Larmor period is associated with interference of different
hyperfine coherences contributing to the dark-state polar-
iton [11].
To test these predictions, we apply a uniform dc mag-
netic field of magnitude 0:5 0:05 G to the atomic en-
semble using three pairs of Helmholtz coils. In our first set
of measurements, 150 ns long coherent laser pulses con-
taining an average photon number 5 serve as the signal
field. The outputs of the single-photon detectors D2 and D3
are fed into two ‘Stop’ inputs of a time-interval analyzer
that records the arrival times with a 2 ns time resolution.
The electronic pulses from the detectors are gated for the
period t
0
;t
0
T
g
, with T
g
240 ns, centered on the
time determined by the control laser pulse during the
retrieval stage. Counts recorded outside the gating period
are therefore removed from the analysis. The recorded data
allow us to determine the number of photoelectric events
N
2
N
3
, where N
i
is the total number of counts in the ith
channel (i 1; 2; 3).
By measuring the retrieved field for different storage
times and orientations of the magnetic field, we obtain the
collapse and revival signals shown in Figs. 2(a)2(e). As
expected, we observe revivals at integer multiples of the
Larmor period. In addition, we see partial revivals at odd
multiples of half the Larmor period, except in the vicinity
of =4. The measured substructures within a single
revival period are in good agreement with the theory (cf.
insets of Figs. 2(e) and 2(j)]. We attribute the overall
damping of the revival signal in the experimental data to
the magnetic field gradients. The evident decrease of this
damping while is varied from 0 to =2 suggests that such
gradients are predominantly along the direction of the
signal field wave vector. Similarly, we attribute the addi-
tional broadening of the revival peaks at longer times to
inhomogeneous magnetic fields, possibly ac fields, not
included in the theoretical description. We are pursuing
additional investigations to determine the temporal and
spatial characteristics of the residual magnetic fields.
Theory predicts that both the collapse and the revival
times (T
C
and T
R
, respectively) scale inversely with the
magnetic field [11]. In Fig. 3 the theoretical prediction
T
C
0:082T
R
(solid line) is compared with the experi-
mentally measured values. We find very good agreement
except for the lowest value of magnetic field B 0:2G,
which may be explained by the presence of residual mag-
netic field gradients.
In the measurements presented above, classical, coher-
ent laser light was used as the signal field [28]. We have
also investigated the revival dynamics of our atomic mem-
ory with the signal field in a single-photon state, as shown
in Fig. 1. The procedure for production of a single-photon
state of the signal field at site A is conditioned on the
detection of an idler photon by D1 (see Refs. [10,26] for
further details). If photoelectric detections in different
channels 1; 2 or 1; 3 happen within the same gating period,
they contribute to the corresponding coincidence counts
between D1 and Dj, N
1j
, j 2; 3. In the absence of the
atomic ensemble at site B, we evaluate the parameter of
Grangier et al. [29], given by the ratio of various photo-
electric detection probabilities that are measured by the set
0
0.05
0.1
(a) - 0
0
0.05
0.1
(b) - /8
0
0.05
0.1
(c) - /4
Retrieval efficiency
0
0.05
0.1
(d) - 3 /8
0 5 10
0
0.05
0.1
(e) - /2
Storage time, s
0 2 4
0.005
0
0.5
1
(f)
0
0.5
1
(g)
0
0.5
1
(h)
0
0.5
1
(i)
0 5 10
0
0.5
1
Storage time, s
(j)
0 2 4
0.05
FIG. 2 (color online). (a)–(e) The ratio of the number of
photoelectric detection events for the retrieved and incident
signal fields for various orientations, 0;=8;=4; 3=8;
=2, of the applied magnetic field, and as a function of storage
time. The incident signal field is a weak coherent laser pulse. In
all cases the control pulse is switched off at T
s
0. We observe
a series of collapses and revivals at multiples of the half Larmor
period of 2:3 s. The observed damping over several Larmor
periods is likely caused by residual magnetic field gradients. The
inset in (e) demonstrates the observed substructure within the
first Larmor period. (f)–(j) Corresponding theoretical plots of
the dark-state polariton number calculated using Eq. (3).
PRL 96, 033601 (2006)
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033601-3
of detectors D1, D2, and D3. For an ideal single-photon
state 0, whereas for coherent fields 1. We have
experimentally determined 0:51 0:06, without any
correction for background or dark counts.
The normalized intensity cross-correlation function g
si
N
12
N
13
=N
R
may be employed as a measure of non-
classical field correlations [19]. Here N
R
N
1
N
2
N
3
R
rep
is the level of random coincidences, where R
rep
25 kHz is the repetition rate of the experiment. The values
of g
si
, obtained by the ratio of the upper and lower traces in
Fig. 4, are well in excess of two at the revival times,
suggesting nonclassical dark-state polaritons. In order to
confirm the violation of the Cauchy-Schwarz inequality
g
2
si
g
ss
g
ii
[29,30], it is necessary to measure intensity
self-correlations for the idler and signal field, g
ii
and g
ss
,
respectively. We have measured, by adding a beam splitter
and an additional detector, the value g
ii
1:42 0:03.
Prohibitively long data acquisition times did not allow
measurement of g
ss
for the revived polariton. Previously
for a 500 ns retrieval time we measured g
ss
2 [10].
In summary, we have demonstrated collapses and reviv-
als of dark-state polaritons in a cold atomic ensemble. The
dynamical manipulation and control of collective matter-
field excitations, at the level of single quanta, is promising
for applications in quantum information science.
We thank M. S. Chapman for discussions and E. T.
Neumann for experimental assistance. This work was sup-
ported by NASA, National Science Foundation, Office of
Naval Research, Research Corporation, Alfred P. Sloan
Foundation, and Cullen-Peck Foundation.
[1] H.-J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, Phys. Rev.
Lett. 81, 5932 (1998).
[2] E. Knill, R. Laflamme, and G. J. Milburn, Nature
(London) 409, 46 (2001).
[3] L.-M. Duan, M. D. Lukin, I. J. Cirac, and P. Zoller, Nature
(London) 414, 413 (2001).
[4] A. Kuzmich and E. S. Polzik, in Quantum Information
with Continuous Variables, edited by S. L. Braunstein and
A. K. Pati (Kluwer, New York, 2003).
[5] M. D. Lukin, Rev. Mod. Phys. 75, 457 (2003).
[6] M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84,
5094 (2000).
[7] D. F. Phillips et al., Phys. Rev. Lett. 86, 783 (2001).
[8] C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, Nature
(London) 409, 490 (2001).
[9] A. Mair et al., Phys. Rev. A 65, 031802 (2002).
[10] T. Chanelie
`
re et al., Nature (London) 438, 833 (2005), and
accompanying Supplementary Information.
[11] S. D. Jenkins et al., Phys. Rev. A (to be published).
[12] S. E. Harris, Phys. Today 50, No. 7, 36 (1997).
[13] M. O. Scully and M. S. Zubairy, Quantum Optics
(Cambridge University Press, Cambridge, England, 1997).
[14] J. Schmiedmayer et al., J. Phys. (France) 4, 2029 (1994).
[15] G. A. Smith et al., Phys. Rev. Lett. 93, 163602 (2004).
[16] C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa,
Phys. Rev. Lett. 69, 3314 (1992).
[17] J. Jacobson et al., Phys. Rev. A 51, 2542 (1995).
[18] M. Fleischhauer and M. D. Lukin, Phys. Rev. A 65,
022314 (2002).
[19] A. Kuzmich et al., Nature (London) 423, 731 (2003), and
accompanying Supplementary Information.
[20] C. H. van der Wal et al., Science 301, 196 (2003).
[21] W. Jiang et al., Phys. Rev. A 69, 043819 (2004).
[22] M. D. Eisaman et al., Phys. Rev. Lett. 93, 233602 (2004).
[23] C. W. Chou, S. V. Polyakov, A. Kuzmich, and H. J.
Kimble, Phys. Rev. Lett.
92, 213601 (2004).
[24] D. N. Matsukevich and A. Kuzmich, Science 306, 663
(2004).
[25] V. Balic et al., Phys. Rev. Lett. 94, 183601 (2005).
[26] D. N. Matsukevich et al., Phys. Rev. Lett. 95, 040405
(2005).
[27] D. Felinto et al., Phys. Rev. A 72, 053809 (2005).
[28] L. Mandel and E. Wolf, Optical Coherence and Quantum
Optics (Cambridge University Press, Cambridge, England,
1995), Chap. 22.
[29] P. Grangier, G. Roger, and A. Aspect, Europhys. Lett. 1,
173 (1986).
[30] D. F. Walls and G. J. Milburn, Quantum Optics (Springer-
Verlag, Berlin, 1994), Chaps. 3 and 5.
0 1 2 3 4 5
0
0
.2
0.4
0.6
0.8
Coincidences rate (s
-1
)
Storage time, s
(a) - 0
0 1 2 3 4 5
0
0
.2
0.4
0.6
0.8
Storage time, s
(b) - /2
FIG. 4 (color online). Squares show the measured rate of
coincidence detections between D1 and D2, 3, N
si
N
12
N
13
as a function of the storage time. Diamonds show
the measured level of random coincidences N
R
. The ratio of
squares to diamonds gives g
si
. Uncertainties are based on the
statistics of the photoelectric counting events.
0
0.2
0.4
0.6
0246
T
C
, µs
T
R
, µs
FIG. 3 (color online). Diamonds show the measured collapse
time T
C
of the first revival at half the Larmor period as a function
of the measured revival time T
R
, for magnetic field values of 0.8,
0.6, 0.4, and 0.2 G, respectively, and for fixed orientation
=2. The line shows the corresponding theoretical prediction
T
C
0:082T
R
from Eq. (3).
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033601-4
    • "The goal is to maximize the storage time of this excitation before it is coherently retrieved by an inverse Raman scattering process. The Larmor precession induced by ambient magnetic field gradients [5] during storage results in dephasing of the retrieved field [6, 7]. This can be offset by writing only the m = 0 states in the stored excitation so that the magnetic field sensitivity is reduced to second order. "
    [Show abstract] [Hide abstract] ABSTRACT: In a cold atomic ensemble the weak Raman scattering of an incident laser beam writes a spin-wave grating by transferring an atom between ground-level hyperfine states. These spin-waves serve as a basis for a quantum memory. For clock states, where magnetic dephasing is suppressed, thermal motion of the atoms across the spin-wave is the principal source of dephasing on the sub-millisecond timescale, limiting the quantum memory time achievable. An investigation of the role of the optical lattice in reducing motional dephasing is presented, using Monte Carlo simulations to study the influence of ensemble temperature, trap depth and differential ac Stark shifts in the case of rubidium.
    Article · Jun 2012
    • "Later we consider the effect of multiple systems. A detailed theoretical description can be found in [9]. We consider a quantum system consisting of two lower states |1 and |2 and an excited state |3 [see Fig. 1(a)]. "
    [Show abstract] [Hide abstract] ABSTRACT: We investigate light storage by electromagnetically induced transparency in a Pr{sup 3+}:Y{sub 2}SiO{sub 5} crystal. The retrieval efficiency versus storage time shows pronounced oscillations, which are due to beating of dark-state polaritons in multiple Zeeman-shifted {Lambda} systems. As a significant obstacle for applications, the beating leads to periodic collapses of the retrieved signal. We demonstrate how to systematically control the perturbing oscillations in the retrieval efficiency by external magnetic fields. This enables suppression of collapses and retrieval of stored data at any storage time, approaching the limit set by the coherence time in the medium.
    Full-text · Article · Jul 2011
    • "3, which shows the amplitude of the retrieved signal associated with the input writing beam W ′ = LG 1 0 + LG 0 0 for different storage times. It is worth noticing that a similar collapses and revivals observation has been reported before and was interpreted as being due to the Larmor precession of the collective spin excitation around the applied magnetic field [27]. Differently from the results presented inFig. 2 , we have observed approximately a four-fold increase in the decay time of the stored coherence grating in the presence of the applied magnetic field. "
    [Show abstract] [Hide abstract] ABSTRACT: We report on the storage of orbital angular momentum of light in a cold ensemble of cesium atoms. We employ Bragg diffraction to retrieve the stored optical information impressed into the atomic coherence by the incident light fields. The stored information can be manipulated by an applied magnetic field and we were able to observe collapses and revivals due to the rotation of the stored atomic Zeeman coherence for times longer than 15mus .
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