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Pi
.rand Optic
Sectio
Section 2
la
hysics
Physics
Section 3
Section 4 Rc
183
184
RLE Progress Report Number 137
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186
RLE Progress Report Number 137
Chapter 1. Quantum Optics and Photonics
Chapter 1. Quantum Optics and Photonics
Academic and Research Staff
Professor Shaoul Ezekiel, Dr. Selim M. Shahriar, Dr. Stephen P. Smith
Visiting Scientists and Research Affiliates
1
2
Dr. Philip R. Hemmer,' Dr. Mara G. Prentiss, John D. Kierstead
Graduate Students
2
John J. Donoghue, 3 Daniel Katz, 2 Juliet Mervis
Undergraduate Students
Arthur Chu 2
1.1 Distributed Fiberoptic Sensor for
Quench Detection in Superconducting
Tokamak Magnets
Sponsor
MIT Plasma Fusion Center
The next generation of magnetic confinement fusion
machines (tokamaks) will use superconducting
rather than conventional magnets for confining and
heating plasmas. These magnets can be longer
than a kilometer and typically cooled using a forced
flow of liquid helium through the conduit which surrounds the superconducting cable. The detection of
a quench, i.e., a section of the magnet going
normal, is important since any increase in heat in
an area caused by an undetected quench could
result in permanent magnet damage. Thus, a quick
and reliable way of detecting such quenches is very
valuable.
Conventional methods for quench detection in
superconducting magnets, such as voltage taps or
monitoring the helium flow in the conduit, have
various limitiations. For example, voltage taps can
have poor signal-to-noise ratio due to inductive
pickup, while helium flow changes caused by a
quench can be slow, depending on the location of
the quench and the length of the magnet.
One novel method for detecting quenches in such a
magnet, is to include an optical fiber with the super4
conducting cable inside the conduit. Since the
optical fiber is in close contact with the cable, any
increase in heat in an area of the cable also causes
heating of the fiber, which can be detected interferometrically.
Figure 1 shows a simplified schematic diagram of a
fiberoptic quench detector. Light from an optical
source is coupled along a single mode optical fiber
and is then sent into two fiber arms using the directional coupler (labeled C1 in the figure). One of
these arms, the sense arm, is co-wound with the
superconducting cable, and the other arm, the reference arm, is held at a constant temperature.
Light from these two arms is recombined using a
second directional coupler (C2) to form a MachAs the sense arm is
Zehnder interferometer.
heated, its optical length increases, and a series of
fringes are observed at the output of the
interferometer. By counting the number and the
direction of these fringes, the change in the integrated temperature along the fiber can be found.
1 Rome Laboratory, Hanscom Air Force Base, Bedford, Massachusetts.
2 Professor, Harvard University, Cambridge, Massachusetts.
3
Tufts University, Medford, Massachusetts.
4 S. Pourrahimi, W.C. Guss, J.V. Minervini, D.B. Montgomery, N.T. Pierce, J.H. Schultz, S.P. Smith, and S. Ezekiel, "US Contributions
to the Development and Calibration of Quench Detectors for the ITER QUELL," Proceedings of the Applied Superconductivity Conference, Boston, Massachusetts, October 17-20, 1994.
187
Chapter 1. Quantum Optics and Photonics
Intensity
Reference
C1
LASER
C2
Sense
Thermal
Perturbations
Optical
Path
Length
(a)
Figure 1.
Initial tests of this fiber interferometer using short
lengths of superconducting wire have demonstrated
that quenches can be easily observed even at liquid
helium temperatures. Figure 2 shows one example
of the data, where initially there is no perturbation
to the optical fiber, and very little drift is observed in
the fringe count. When a current is introduced into
the superconducting wire, as indicated by the slight
rise in the voltage across the wire (due to ohmic
losses in the leads), very little change is observed
in the fringe count. However, when the superconductor is quenched, using a current pulse applied to
a heater wrapped around a short section of the
superconducting wire, a large rise in the voltage
across the superconductor is observed, and the
fringe count rises dramatically. Finally, when the
current is stopped in the superconducting wire, the
fringe count abruptly drops to near its pre-quench
level.
There are a number of issues with this sensor that
still need to be investigated including reduction of
the sensitivity of the optical fibers to changes in
cable strain, survival of the optical fibers through
the manufacturing of the superconducting cable,
and extraction of the fibers from the magnets.
Preparations are currently underway to test this
quench detection scheme and a number of others
in a 100 meter superconducting cable. This test is
part of ITER, an international scientific collaboration
on fusion research between the United States,
Japan, the European Union, and the Russian Federation. This test cable will be manufactured in
Japan with sensors provided by the United States.
The tests will be carried out in Switzerland.
188
RLE Progress Report Number 137
Fringe
Count
1600
50s.
bt
Superconductor
Voltage
Quench
Heater
Voltage
5
Figure 2.
1.2 Measurement of Liquid Helium Flow
in Superconducting Tokamak Magnets
Sponsor
MIT Plasma Fusion Center
The accurate measurement of liquid helium flow is
important in a number of experiments and applications involving superconducting magnets. Conventional measurement techniques such as venturis or
orifice plates have a number of drawbacks including
a small dynamic range, constriction of the flow,
Chapter 1. Quantum Optics and Photonics
poor bidirectional response, and poor transient
response.
A new optical technique is being investigated for
the measurement of the liquid helium flows. This
technique has the advantages of a very large
accuracy,
inherent
dynamic
range,
high
bidirectionality, virtually no constriction or disruption
of the flow and, in contrast with laser Doppler
velocimetry, does not require a seeded flow.
counterpropagating flow. Thus, the flow will cause a
difference in the optical path length for the two
beams, resulting in a phase shift between the two
beams. Figure 5 shows an example of how this
system could be implemented with only minimal disruption of the flow. In this case, the interferometer
will measure the component of the flow along the
direction of light propagation.
This flow measurement technique is based on the
change in the speed of light in a moving medium,
referred to as Fresnel drag.5 The relativistic calculation gives the speed of light in a moving medium,
cm, as:
+U
do/n
m 1 + u/nco
co
n
1
n I
where c, is the speed of light in vacuum, n is the
index of refraction of the medium, and v is the
velocity of the flow along the direction of light propagation. Thus, for a 1 m/s flow in liquid helium the
fractional optical path length change, AL/UL, resulting
from this change in the speed of light is only about
Figure 3.
2 x 10- 10.
One method for measuring this small effect uses a
Sagnac interferometer (shown in figure 3).6 Light
from a source is coupled into a single mode optical
fiber and then is split into two beams by a fiber
coupler C and the beams are then sent in opposite
directions around a fiber ring. The beams are then
recombined using the same coupler C and the
resulting intensity is measured using detector D.
However, in contrast with either a Michelson or
Mach-Zehnder interferometer, since both beams
travel along the same path, any change in optical
path length, for example due to fiber temperature or
strain changes, is the same for both beams so that
the effect is reciprocal, and results in no change in
the output intensity. Only effects which are nonreciprocal, i.e., different for the two directions of
propagation, will result in a change in the output
intensity.
Fresnel drag, as discussed above, is one such nonreciprocal effect. As shown schematically in figure
4, the light in the clockwise (CW) direction experiences a copropagating flow while the light in the
counterclockwise (CCW) direction experiences a
Figure 4.
Liquid Helium
Figure 5.
Initial calculations indicate that this technique could
be used for liquid helium flows on the order of 1
m/s with very small or negligible perturbation to the
5 R.T. de Carvalho and J. Blake, "Slow-flow Measurements and Fluid Dynamics Analysis Using Fresnel Drag Effect," Appl. Opt. 33:
6073-6077 (1994); G.A. Sanders and S. Ezekiel, "Measurement of Fresnel Drag in Moving Media Using a Ring-resonator Technique," J. Opt. Soc. Am. B 5: 674-678 (1988).
6 J.L. Davis and S. Ezekiel, "Closed-loop, Low-noise Fiber-optic Rotation Sensor," Opt. Lett. 6: 505-508 (1981).
189
Chapter 1. Quantum Optics and Photonics
flow. In addition, the sensor is inherently
bidirectional, virtually immune to electro-magnetic
interference, and insensitive to temperature and
mechanical perturbations. It also has a very high
dynamic range and a very low sensitivity to magnetic fields. Experiments are currently underway to
study this type of flow meter using several
cryogenic liquids.
1.3 Efficient, Low-Intensity Optical
Phase Conjugation using Coherent
Population Trapping in Sodium
Sponsor
U.S. Air Force - Electronic Systems Division
Contract F19628-92-K-0013
intensities accessible with cw diode lasers, opening
the possibility of the development of portable, high
speed, four-wave mixing devices.
To see how CPT can be used to perform OPC,
consider the four-level double A system of figure 6a
in the traditional phase conjugation geometry of
figure 6b. The two A subsystems are assumed to
be separate. For simplicity, consider only the case
where F and S saturate the two-photon transition
and B and C are weak. The A subsystem involving
F and S and the states Ia >, Ib >, and le > gets
optically pumped into a transparent superposition of
the ground states. This corresponds to a purely
sinusoidal grating in the phase of the ground state
coherence. The important property of this grating is
that it can be saturated at optical intensities well
below those needed to saturate the individual
optical transitions.
We have observed optical phase conjugate gain
(>50) in sodium vapor using low intensity pump
lasers (1 W/cm 2), with a response time on the order
of 1 psec.7 We have experimentally identified
coherent population trapping (CPT) as the phase
conjugate mechanism. We have also developed a
theoretical model which supports these observations by showing that coherent population trapping
can write large amplitude, nonlinear optical gratings
at laser intensities well below those needed to saturate the optical transitions.
Four-wave mixing and optical phase conjugation
(OPC) have long been known to have potential
applications to optical image amplification, processing and aberration correction. However, widespread application of these techniques has so far
been limited because of the slow response and/or
low efficiency of existing nonlinear optical materials
at laser intensities achievable with compact cw
lasers. For example, previous work in sodium vapor
shows fast response, 8 but phase conjugate gain is
observed only at high pump intensities (in the range
of 100 W/cm 2).9 We have demonstrated high efficiency OPC in sodium for pump intensities near 1
W/cm 2, with a response time on the order of 1
psec. If sodium were replaced by rubidium or
cesium, a similar performance could be achieved at
(a)
F
,
F
\ le>
F
C
la>
(b)
B
C
Ib>
Ib>
Figure 6. (a) Schematic of four-level double A system.
(b) Corresponding four wave mixing geometry.
To produce the conjugate beam C, the read beam
B scatters off of the grating formed by F and S. For
the special case where all lasers are resonant with
the excited states, the conjugate wave amplitude C
only increases until the four-level closed-loop transparency condition is approached. After this, B and
C propagate as though the medium were transparent. In the more general case, for example, off
resonant lasers and strong forward and backward
pumps F and B, preliminary calculations show that
high gain is possible. In the case of a pure three-
7 P.R. Hemmer, M.S. Shahriar, D.P. Katz, J. Donoghue, P. Kumar, and M. Cronin-Golomb, "Efficient Low-Intensity Optical Phase
Conjugation Based on Coherent Population Trapping in Sodium," Opt. Lett. 20: 982 (1995).
8
C.J. Gaeta, J.F. Lam, and R.C. Lind, Opt. Lett. 14: 245 (1989).
9 M. Vallet, M. Pinard, and G. Grynberg, Opt. Comm. 81: 403 (1991); J.R.R. Leite, P. Simoneau, D. Bloch, S. Le Boiteux, and M.
Ducloy, Europhys. Lett. 2: 747 (1986).
190
RLE Progress Report Number 137
Chapter 1. Quantum Optics and Photonics
LASER
F
A/O
LASER
B
RF
SODIUM
S
C
C BDETS.
B
S
DF
ETS.
Figure 7. Schematic of experimental setup. Laser beam
S is derived from F with an acoustic optic modulator
(A/O), driven with a stable rf source.
level system, this scheme still works as long as B
and S are nondegenerate.10
The experimental apparatus used to perform OPC
using CPT is schematically shown in figure 7. The
sodium vapor cell is a heat pipe oven operated at
about 200' C with 5 mtorr of He buffer gas and a
variable interaction length of 6 to 12 cm which is
magnetically shielded to better than 100 mGauss.
Two ring dye lasers generate the forward and backward pumps F and B, as shown. Both lasers are
tuned approximately to the D1 transition. The
signal beam S is derived from F using an acoustooptic modulator (A/O) configured for upshifting and
driven with an rf signal of 1.77 GHz having about 1
kHz frequency jitter. This ensures that the laser
jitters of F and S are correlated as required for efficient CPT." Laser beams F and S typically enter
the active medium with a 4 mrad angular separation. In addition, the backward pump B is also
aligned about 3 mrad away from counterpropagating with F in a direction perpendicular to the F
and S plane. This prevents optical feedback of one
laser into the other while maintaining the Bragg
angle. Typical spot sizes in the cell are about 1.6
mm FWHM for B, 1.0 mm for F, and 1.0 mm for S.
Pump intensities (F and B) are in the range of 1 W/
cm2 . All of the beams are detected in transmission
through the cell. Finally, the frequency reference is
provided by an atomic beam (not shown).
Figure 8a shows a scan of the conjugate gain R
(reflected power/input signal power) and transmitted
signal gain T as a function of the frequency of the
forward pump laser F. Note that the frequency of
laser S is also scanned since S is generated from F
with the A/O. As shown, high gains are observed,
both in reflection and transmission. Here, the peak
conjugate gain of 55 occurs when F is blue detuned
about 200 MHz from the F=2 <-> F'=2 transition
frequency, S is upshifted from F by 1774 MHz, and
B is red detuned about 600 MHz from the F=1 <->
F'=2 transition. For this data, the optical intensity of
the forward and backward pumps F and B are 1.2
and 0.5 W/cm 2, respectively, and the signal beam S
has an intensity of 3.5 mW/cm 2. This data shows a
factor of 16 increase in reflectivity over previous
sodium vapor experiments at about 1 percent of the
pump intensity. For this data, the shortest interaction length of 6 cm is used. Using a longer interaction length of 12 cm and higher pump intensities
(5 W/cm 2), conjugate reflectivities well above 100
are observed (not shown). The response time is
measured by switching the rf signal to the A/O and
monitoring the phase conjugate reflection. We find
that the response time is no slower than 1.4 psec,
the measurement being limited by the speed of the
rf switching electronics.
Figure 8b shows a scan of the conjugate gain R as
a function of the frequency detuning of S relative to
F, obtained by scanning the rf frequency applied to
the A/O (see figure 7) while compensating for alignment changes. All other conditions correspond to
the peak gain in figure 6a. The observed difference
frequency width of the gain is about 2.3 MHz (centered near 1774 MHz), which is to be compared
with the 10 MHz natural linewidth of sodium. This
subnatural rf frequency linewidth provides evidence
of Raman CPT. 12 Frequency measurements of the
conjugate beam C show that it is downshifted from
the backward pump B by 1774 MHz. When B and
C are combined on a fast photodiode, a narrow 2
kHz beat note is observed (near the 1 kHz rf linewidth), even though beams F and B are derived
from independent lasers, each having about 50
MHz absolute frequency jitter. This narrow beat is
evidence of the closed-loop model.
In summary, we have observed high-phase conjugate gain (R > 50) in sodium vapor at low pump
intensities (-1 W/cm 2), with a fast response time
(-1 psec). Raman coherent population trapping has
been experimentally identified as the physical basis
of the conjugate generation process. This excellent
10 M.S. Shahriar, P.R. Hemmer, J. Donoghue, M. Cronin-Golomb, and P. Kumar, OSA Annual Meeting Technical Digest (Washington,
D.C.: Optical Society of America, 1992), v. 23, p. 127.
11 J.E. Thomas, P.R. Hemmer, S. Ezekiel, C.C. Leiby, Jr., R.H. Picard, and C.R. Willis, Phys. Rev. Lett. 48: 867 (1982).
12M. Poelker and P. Kumar, Opt. Lett. 17: 399 (1992).
191
Chapter 1. Quantum Optics and Photonics
performance opens the possibility of developing
practical, portable, high-gain optical signal processing devices, based on optical phase conjugation
or four-wave mixing.
(a)
37i0 J
55-
I
I
F=1
2
LASER F FREQ.
t
(b)
2.3 MHz
RF FREQ.
-
Figure 8. (a) Signal gain T and phase conjugate gain R
versus laser F frequency. The frequency scale is labeled
by the transition frequencies corresponding to the F=1
and F=2 ground state hyperfine components. (b) Phase
conjugate gain R versus rf frequency driving the acousto
optic modulator.
1.4 Highly Selective Nonspatial-Filters
Using Porous Matrix Based Thick
Holograms
Sponsor
Ballistic Missile Defense Organization
Grant NG0921-94-C-0101
We have developed a novel technique for laser
beam cleanup, the nonspatial filter, 13 which is based
on the Bragg selectivity of thick holograms. This
technique eliminates the need for laser beam
focusing, which is the source of many of the alignment instabilities and laser power limitations of
spatial filters. Standard holographic materials are
not suitable for this application because differential
shrinkage during processing limits the maximum
Bragg angle selectivity attainable. We have developed a new technology which eliminates this
problem.
Preliminary results show an angular
selectivity of less than one milliradian.
For practically any application, the laser beam
should be as clean as possible. Currently, this is
accomplished by spatial filtering. 14 There are two
types of spatial filters in widespread use. The most
common is the so-called "pinhole" filter, which consists of a lens with a pinhole in the focal plane. For
more demanding applications, the pinhole is
replaced by a single-mode optical fiber. One major
problem with both the pinhole and fiber spatial
filters is their requirement for matching a tightly
focused laser beam to a small target. Moreover,
both pinhole and fiber spatial filters are problematic
when used with high-power lasers. In the case of
pinhole spatial filters, a focused high-power laser
can machine its own pinhole (of nonoptimal size).
For this reason, spatial filters for high-power lasers
are often aligned with the power turned down.
However, if the pinhole position is inadvertently
shifted during high-power operation, the holeburning problem returns. The situation is worse for
fiber spatial filters, since even a moderate intensity
laser beam can produce nonlinear optical interactions when focused into the small optical fiber
core, for example Brillouin and Raman scattering
and refractive index changes due to increases in
heating.
To solve the numerous problems inherent in spatial
filters, we have developed nonspatial filtering. The
basic idea of nonspatial filtering is similar to that of
spatial filtering. Specifically, note first that a laser
beam with arbitrary spatial variations in intensity
can be expressed as linear combinations of plane
waves (or some other basis functions). In spatial
filters, a Fourier transform lens is used to convert
angle into position in order to separate the spatial
components.
In contrast, nonspatial filtering is
done directly on the laser beam angle. A filter
13 J.E. Ludman, J. Riccobono, J. Caulfield, J. Fournier, I. Semenova, N. Reinhand, P.R. Hemmer, and M.S. Shahriar, "Porous Matrix
Holography for Non-Spatial Filtering of Lasers," Proceedings of the IEEE Symposium on Electronic Imaging: Science and
Technology, San Jose, California, 1995.
14 E. Hecht and A. Zajac, Optics (Reading, Massachusetts: Addison-Wesley, 1975).
192
RLE Progress Report Number 137
Chapter 1. Quantum Optics and Photonics
element is inserted in the laser beam path to selectively deflect light waves propagating at a particular
angle, throwing away the unwanted light (as does
the spatial filter).
In particular, we use a thick
hologram as the filter element. The Bragg selectivity of such a hologram guarantees that only
waves propagating at a particular angle (the Bragg
angle) get deflected. Two-dimensional filtering can
be achieved by using two such holograms.
We consider here the special case in which nothing
is absorbed, and where only the phase of the wave
gets modulated, due to the presence of index modulation.
For a monochromatic hologram with a
grating periodicity of A, the angle of incidence, 0 B
for perfectly phase matched Bragg diffraction is
given by Sin(OB) = A/2nA, where A is the wavelength of incident light, and n is the average index
of refraction of the hologram.1 5 The diffraction efficiency, rj, for TE polarization, is then given by j =
Sin 2{rrnid/ACos(0)}. Here, n, is the amplitude of
the sinusoidal index modulation, and d is the thickness of the hologram. For TM polarization, the
effective value of the index modulation is reduced
by a factor of Cos(28). The smallest value of n, for
which maximum diffraction can be obtained thus
varies inversely with the thickness and is very small
for a thick hologram.
The angular selectivity (FWHM) is given by
AO , A/d. Thus, in order to maximize the angular
selectivity, one has to choose as small a wavelength as possible for writing the hologram and
make the hologram as thick as possible. Both of
these factors are of course limited by practical considerations. For example, residual loss may limit
the maximum usable thickness.
Standard holographic materials are not suitable for
this application because differential shrinkage
during holographic processing limits the maximum
Bragg angle selectivity attainable by affecting the
Bragg angle in a nonuniform manner. Differential
shrinkage occurs because processing usually
requires the addition or removal of molecules
through the surface of the material, thus leading to
shrinkage, which depends on the distance from the
surface of the material. What is needed is a
holographic structure with negligible differential
shrinkage. The technology we have developed is
based on the use of a rigid porous substrate material, porous glass. An active light sensitive material
such as holographic photopolymer is loaded into
the rigid host structure. The size of the pores is
much smaller than the optical wavelength, and the
index of modulation is small.
We made a thick hologram using porous glass,
which contains Boron, Sodium, and about 70
percent SiO 2 (before being rendered porous). The
light sensitive material used is a holographic
photopolymer. 16 The average pore diameter is
about 300 A. The hologram was recorded using a
wavelength of 488 nm, resulting in about 2000
lines/mm. The thickness of the hologram is about
0.7 mm. The hologram was found to be most transparent (96 percent) at 1500 nm, a wavelength of
particular interest in fiberoptic communications.
The transparency drops on either side of this wavelength. For example, at 1900 nm the transparency
is about 50 percent, while at 540 nm it is about 70
percent.
We tested the performance of this hologram using a
He-Ne laser. At this wavelength (632.8 nm), the
transparency is close to 75 percent. To measure
angular selectivity, we mounted the hologram on a
rotation stage and measured the diffracted power
as a function of the incidence angle. We found an
angular selectivity of about 0.8 milliradian, which is
close to the theoretically expected value of about
0.7 milliradian. This small difference may be attributed to the finite resolution of the rotation stage,
as well as the finite divergence of the test beam.
To demonstrate nonspatial filtering in one dimension, we used a Gaussian beam from a He-Ne
laser as the input beam. In order to compare the
transmitted beam profile with that of the diffracted
beam, we did not add any index matching fluid so
that the transmitted and diffracted beams could be
of comparable intensity. The profiles of the transmitted (top) beam and the diffracted (bottom) are
shown in figure 9. The image was taken with a ccd
camera and recorded on a video tape. A frame
grabber was then used to digitize the image. As
can be seen clearly, the beam has the same width
in the horizontal direction but is much narrower in
the vertical direction (the direction of diffraction).
Thus, the beam has been cleaned in the vertical
direction but not in the horizontal direction. Figure
10 shows the horizontal (top) and vertical (bottom)
cross section of the diffracted beam. As can be
seen, the width (FWHM) in the vertical direction is
about one-fifth of the width in the horizontal direc-
15 H. Kogelnik, "Coupled Wave Theory for Thick Hologram Gratings," Bell Sys. Tech. J. 48: 2909-2947 (1969).
16
D.H. Whitney and R.T. Ingwall, "The Fabrication and Properties of Composite Holograms Recorded in DMP-128 Photopolymer,"
Proc. SPIE 1213: 18 (1990).
193
Chapter 1. Quantum Optics and Photonics
0
50
50
Figure 9. Profiles of the transmitted (top) and diffracted
(bottom) spots through the one-dimensional thick
hologram.
tion, with a residual divergence of about 0.8
milliradian.
To summarize, we have demonstrated nonspatial
filtering with a thick hologram made in a porous
glass host. We have demonstrated an angular
selectivity of about 0.8 milliradian, which is in close
agreement with theoretical predictions. Future work
will include demonstration of nonspatial filtering in
two dimensions, further enhancement of angular
selectivity, and reduction in absorption. The thick
holograms we have developed may also be of use
for other applications, such as holographic optical
data storage, spectroscopy, and intracavity laser
mode selection.
1.5 Cache Memory using Optically
Induced Spin Echo
Sponsor
U.S. Air Force - Electronic Systems Division
Contract F19628-92-K-0013
194
RLE Progress Report Number 137
100
100
200
150
150
250
200
300
250
Figure 10. Horizontal (top) and vertical (bottom) cross
sections of the diffracted beam, demonstrating an angular
selectivity of 0.8 mrad.
Optical computers and neural networks require the
ability to store, process, and interconnect highresolution 2D (and 3D) optical data entering at high
frame rates. Currently, high-speed 2D images can
be stored (for later readout and processing at
slower rates) using high-speed video cameras.
Commercially available cameras can store 30
frames at 1 MHz or 8 frames at 10 MHz, and effectively act as optical cache memories. To store 3D
images, high-speed holographic techniques can be
used. Holographic cinematography can store 4000
medium-resolution holograms at 300 kHz frame
rates or 40 high-resolution holograms at 20 kHz
frame rates. Optical spectral hole-burning materials
can be used to both store and process 2D and 3D
optical images at high frame rates. So far, optical
photon echoes have been used to perform mediumresolution pattern recognition at a 30 MHz frame
Chapter 1. Quantum Optics and Photonics
rate, 17 and to store 1600 optical data bits (at 8 a
single spatial location) with a 40 MHz frame rate.'
Optical spectral hole burning has limitations,
however. For example, slow readout for interfacing
to optoelectronic devices would require a gated
detection scheme and multiple reads of the entire
memory contents. While 10 read cycles at a single
point has not been found to significantly degrade
the stored data, the 1000 read cycles required to
separately read 1000 images would be expected to
cause image degradation, especially for highresolution data. Also, although data storage times
for stimulated optical echoes can exceed hours,19
the total duration of the input optical data stream
cannot be longer than 1 msec. This limits the
number of images that can be stored at frame rates
Even to achieve this
slower than 10 MHz.
maximum 1 msec duration, a very stable laser is
needed so that the laser will remain approximately
phase-coherent. Finally, there are potential limita-
tions due to the low readout efficiency (about 10- 5
of the input image strength). 18
We have designed a high-speed optical cache
memory 20 which should have similar performance to
optical echo memories (i.e., capability of storing
1000 seccessive holographic images at frame rates
up to 10 MHz), but without many of their limitations.
For example, slow readout should be possible
without multiple reads (and hence partial erasure)
of each image. This memory should also be
capable of storing optical data streams of duration
much longer than 1 msec without the need for
maintaining absolute laser phase coherence (i.e.,
noisy lasers can be used). Finally, theoretical efficiencies are higher than for optical spectral hole
burning.
This design is based on our recent demonstration
of the ability of Raman coherent population trapping
to store and recall optical temporal and phase information using spin echoes (in a sodium atomic
beam). 21 In this experiment, two optical data pulses
are used as input, each pulse consisting of twofrequency Raman-resonant laser light. Both of
these Raman optical pulses create spin coherences
via Raman population trapping. 22 The population
trapping process also allows for these spin coherthe
storing
thereby
interfere,
to
ences
temporal/phase information. Any technique applicable to spin echoes can be used to rephase the
spin coherences, for example an rf Tr-pulse or an
off-resonance Raman Tr-pulse. The rephased spin
coherences are then detected optically using a twofrequency Raman resonant probe. The spin echo
leads to an experimentally observed decrease or
increase in probe absorption, depending on the relative optical phase.2 1
Slow readout of the stored optical images can be
achieved by noting that the maximum input/output
data rate in a spin-echo memory is determined by
the magnitude of the inhomogeneous broadening of
the rf spin-transition. Since most spin-echo materials have small intrinsic inhomogeneous broadening (about 1 - 10 kHz), their speed is determined
primarily by the strength of an applied magnetic
field gradient. For example, a 2 kGauss/cm magnetic field gradient and a 5 kHz/Gauss magnetic
Zeeman shift should permit an input data rate of 10
MHz over a 1 cm sample of spin-echo material.
However, reducing the magnetic field gradient to 2
Gauss/cm gives a 10 kHz output data rate. This is
illustrated in figure 11.
17 X.A. Shen and R. Kachru, "High-speed Pattern Recognition by Using Stimulated Echoes," Opt. Lett. 17: 520 (1992).
18 Y.S. Bai and R. Kachru, "Coherent Time-domain Data Storage with a Spread Spectrum Generated by Random Biphase Shifting,"
Opt. Lett. 18: 1189 (1993).
19 M. Mitsunaga, R. Yano, and N. Uesugi, "Time- and Frequency-domain Hybrid Optical Echo Memory: 1.6-kbit Data Storage in
Eu3 :Y2SiO s ," Opt. Lett. 16: 1890 (1991).
20
M.S. Shahriar, P.R. Hemmer, and M.K. Kim, "Five Dimensional Optical Data Storage," submitted to Opt. Comm.
21 P.R. Hemmer, M.S. Shahriar, M.K. Kim, K.Z. Cheng, and J. Kierstead, "Time Domain Optical Data Storage using Raman Coherent
Population Trapping," Opt. Lett. 19, 296 (1994).
22 M.S. Shahriar and P.R. Hemmer, "Direct Excitation of Microwave-spin Dressed States Using a Laser-excited Resonance Raman
Interaction," Phys. Rev. Lett. 65: 1865 (1990).
195
Chapter 1. Quantum Optics and Photonics
F write
•ih
DATA
I-
n- PULSE
nread
1 L
[]
READ-OUT
rread
[B]
n- PULSE
SLOWER READ-OUT
Figure 11. Schematic illustration of the variable speed read-out of spin echo: (a) Data stream stored, time-reversed,
and read at a high speed using a large spin inhomogeneous broadening, created by a magnetic field gradient; (b)
Slower read-out if the inhomogeneous broadening is reduced during rephasing.
The duration of the input data stream is not limited
by the optical coherence lifetime, but by the spin
coherence lifetime which can be much longer than
the 1 msec limit for optical echoes. For example, in
Eu 3 +:Y 2 SiO 5 crystal at 2 K, the spin population lifetime can exceed hours and spectral diffusion is also
very small. Thus, it is reasonable to expect that
spin coherence lifetimes on the order of seconds or
longer should be possible. Moreover, since Raman
coherent population trapping is not very sensitive to
correlated laser frequency jitter, the laser stability
requirement can be greatly relaxed if, for example,
laser field 2 is generated from field 1 with acoustooptic or electro-optic devices.
To summarize, we have designed a novel highspeed optical cache memory which is capable of
storing about 1000 successive holographic images
at frame rates up to 10 MHz and allows a much
slower read-out. Experiment is in progress using a
dye laser and a Eu3 +:Y 2SiO 5 crystal cryogenically
cooled to superfluid He temperature to demonstrate
this memory.
23
1.6 Doppler Cooling in Traveling Wave
Velocity Selective Coherent Population
Trapping
Sponsor
U.S. Navy - Office of Naval Research
Grant N0014-91-J-1808
Recently, there has been increasing interest in
cooling atoms to ultralow temperatures for potential
applications to spectroscopy, improved atomic
clocks, and observation of quantum collective
effects such as Bose-Einstein condensation. One
promising candidate is a system of A type atoms
excited by two counterpropagating traveling waves.
It has been shown previously that such a system
cools to a temperature far below the recoil limit.
However, velocity selective coherent population
trapping (VSCPT), occurs via random walks in
momentum space and therefore is extremely slow.
This makes it nearly impossible to achieve subrecoil cooling in three dimensions. What is needed
is to provide additional frictional forces that coexist
with this process. However, theoretrical calculations
showed that no such frictional force exists in this
system for any choice of parameters.2 3
A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, Phys. Rev. Lett. 61: 826 (1988).
196
RLE Progress Report Number 137
Chapter 1. Quantum Optics and Photonics
We have found that this theoretical prediction was
incorrect,24 and have identified conditions under
which a frictional cooling force exists. In a semiclassical view, this force is found to exist in the
transient regime of the optical Bloch equations.
However, we have also shown that this frictional
cooling is actually continuous when a fully quantized model is used. This additional cooling force is
expected to accelerate the process of VSCPT
enough to achieve a sub-recoil temperature in three
dimensions.
Figure 12 illustrates the physical origin of this
cooling force. Consider the case where, in the lab
frame, both fields are equally detuned to the red,
and the atom is moving opposite to the oa polarized
beam at a velocity v. In the atom's rest frame, the
o-_ beam is tuned closer to the resonance, while the
o- beam is tuned farther away from resonance. It
turns out, however, that even under this broken
symmetry there is no semiclassical friction force in
the steady state. We have interpreted this result
physically using cascaded adiabatic following arguments. The steady state coherence is such that the
expectation value of the force operator identically
vanishes.
However, in the transient regime, more photons are
absorbed (and randomly remitted) from the ao
beam than the other one. Therefore, the atom
This semi-classical result, however, is not valid
when the atoms become so cold that the de Broglie
wavelength becomes comparable to the laser wavelength. Therefore, it is necessary to examine this
process in a model in which the atom's position and
linear momentum are fully quantized. We performed this calculation and found that the cooling
takes place even in the model. More important, the
model predicts that this additional cooling process
Therefore,
is not transient, but is continuous.
VSCPT under the condition of red detuning is
expected to be significantly more efficient.
To summarize, we have found that, contrary to previous assertions, frictional cooling force does exist
in traveling wave VSCPT if the beams are red
detuned. This may prove useful in enhancing the
rate of VSCPT in three dimensions. Experimental
work is in progress for using this effect, as well as
the alternative method of standing wave VSCPT, to
achieve subrecoil cooling in three dimensions, using
87 Rb atoms and semiconductor lasers.
a
a
lab
experiences cooling until the steady state is
reached. This is illustrated in figure 13. For parameters of experimental interest, this transient process
lasts about as long as the time scale for the
polarization gradient cooling. The cooling coefficient
is comparable to that of conventional Doppler
cooling for a two level atom.
frame
atom
Lb
frame
Figure 12. Physical origin of the transient cooling force in traveling wave VSCPT for red detuning.
24
M.S. Shahriar, M.G. Prentiss, and P.R. Hemmer, "Transient Heating and Cooling in Travelling Wave Velocity Selective Coherent
Population Trapping," OSA Annual Meeting Technical Digest, (Washington, D.C.: Optical Society of America, 1994), v. 25, p. 159.
Chapter 1. Quantum Optics and Photonics
The uncertainty in one quadrant, however, may be
arbitrarily small, provided the uncertainty in the
other quadrant is allowed to grow correspondingly
larger. Phase sensitive detection of the quadrant
with the reduced variance thus may be used to
perform measurements below the shot noise limit.
Fields that have suppressed variance in one
quadrature are called squeezed states and can be
generated via multi-wave mixing processes in a
nonlinear medium.
xE-2
1.81
-F(t)
---Aug. T(t
--Doppler
I
U
-1.81
-3.N
I
I
TIfE ---)
Figure 13. Illustration of the duration and magnitude of
the transient cooling force for traveling wave VSCPT
under red detuning. The force is in units of hk/F, and
time duration is 80 F-1. In the fully quantized model, this
cooling is seen to be continuous.
1.7 Near-perfect Squeezing in a Folded
Three-Level System
Sponsor
U.S. Air Force - Electronic Systems Divisions
Contract F19628-92-K-001 3
In many applications involving lasers, the ultimate
accuracy of measurement is limited fundamentally
by the shot noise. The shot noise is a consequence of the quantum nature of light, and results
from the Heisenberg uncertainty principle. The
output of a conventional laser is the coherent state,
which closely resembles a classical electromagnetic
field. However, the strength of the electric field
amplitude, for example, can not be measured precisely. In particular, the two quadratures of the
sinusoidally oscillating field are conjugate quantum
variables, and the product of the variance for the
two quadratures is limited by Planck's constant.
To date, the best material for generating squeezed
states have been crystals with X2 type nonlinearity.
However, this medium is inappropriate for applications involving detection of very weak images
because phase matching constraints severely limit
the spatial bandwidths of image squeezing.25 What
is needed is a material with X3 type nonlinearity,
which yields perfect phase matching for any configuration, which in turn implies very large spatial
bandwidth for image squeezing. One such material
is a two-level atom. The noise from spontaneous
emission strongly degrades squeezing in such a
system, however.
We have performed calculations showing that near
perfect squeezing can be achieved if a A system is
used instead of a two level system. 26 This system
possesses strong X3 type nonlinearity, but does not
have problems of noise from spontaneous emission. This is because Raman type strong gain can
be generated via ground states coherence, without
much optical coherence. Figure 14 illustrates the
field configuration to be used for observing this
squeezing. Here, F and B are the forward and
backward pumps, respectively, in a phaseconjugate geometry, S is the probe, and C is the
conjugate. When mixed with the local oscillator, a
superposition of the signal and conjugate beams
yields quadrature squeezing in a configuration
similar to the one used by Slusher et al. for a two
level system.2 7 Note that unlike other predictions,2 8
this system does not assume a nonzero decay rate
of the ground states and can be easily realized for
example, using a j=1 <-> j'=l transition.
To summarize, we have found that near perfect
squeezing can be achieved in a X3 phase matched
25 P. Kumar and M.I. Kolobov, "Degenerate Four-wave Mixing as a Source for Spatially-broadband Squeezed Light," Opt. Comm. 104:
374 (1994).
26 M.S. Shahriar, P.R. Hemmer, and P. Kumar, "Detailed Theory of Near-perfect Squeezing Using an Ideal A System," to be submitted
to Phys. Rev. A.
27 R.E. Slusher, L.W. Hollberg, B. Yurke, J.C. Mertz, and J.F. Valley, Phys. Rev. Lett. 55, 2409 (1985).
28
C.M. Savage and D.F. Walls, "Squeezing Via Two-photon Transitions," Phys. Rev A 33: 3282 (1986).
198
RLE Progress Report Number 137
Chapter 1. Quantum Optics and Photonics
four wave mixing geometry using a pure A system.
Experimental work is under progress to observe this
effect in sodium using dye lasers, and in rubidium
using semiconductor lasers. Twin beams generated this way may help improve the signal to noise
ratio in the large angle atomic beam splitter demon29
strated by us.
........
.....
........
...
S-
.........
e
\
F
LO
C\
Figure 14. Schematic illustration of the level structure
and optical fields to be used in generation of squeezed
states via four wave mixing, using a A system. F: forward
pump, B: backward pump, S: probe, C: conjugate, LO:
local oscillator.
29 K. Johnson, A. Chu, T. Lynn, K. Barggren, M.S. Shahriar, and M. Prentiss, "Demonstration of a Non-magnetic Blazed Grating Atomic
Beam Splitter," Opt. Lett., forthcoming.
199
Professor Daniel Kleppner, Associate Director of the Research Laboratory of Electronics (Photo by John F.
Cook)
200
RLE Progress Report Number 137