An experiment is described which is an analog of Young\u27s double-slit interferometer using an atomic electron instead of light. Two phase-coherent laser pulses are used to excite a single electron into a state of the form of a pair of Rydberg wave packets that are initially on opposite sides of the orbit. The two wave packets propagate and spread until they completely overlap, then a third phase-coherent laser pulse probes the resulting fringe pattern. The relative phase of the two wave packets is varied so that the interference produces a single localized electron wave packet on one side of the orbit or the other

Noel, Michael W.

Stroud, C. R., Jr.

English

Scholarship;  Research;  and Creative Work at Bryn Mawr College

Bryn Mawr College
Scholarship, Research, and Creative Work at Bryn Mawr
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Physics Faculty Research and Scholarship Physics
1995
Young's Double-Slit Interferometry within an Atom
Michael W. Noel
Bryn Mawr College, mnoel@brynmawr.edu
C. R. Stroud Jr.
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Michael W. Noel and C. R. Stroud, Jr., "Young's double-slit interferometry within an atom," Phys. Rev. Lett. 75, 1252 (1995).
VOLUME 75, NUMBER 7 PH YS ICAL REVIEW LETTERS 14 AUGUsT 1995
Young's Double-Slit Interferometry within an Atom
Michael W. Noel and C.R. Stroud, Jr.
The Institute of Optics, University of Rochester, Rochester, New York 14627
(Received 10 April 1995)
An experiment is described which is an analog of Young's double-slit interferometer using an atomic
electron instead of light. Two phase-coherent laser pulses are used to excite a single electron into a
state of the form of a pair of Rydberg wave packets that are initially on opposite sides of the orbit. The
two wave packets propagate and spread until they completely overlap, then a third phase-coherent laser
pulse probes the resulting fringe pattern. The relative phase of the two wave packets is varied so that
the interference produces a single localized electron wave packet on one side of the orbit or the other.
PACS numbers: 03.75.Dg, 32.80.Rm, 42.25.Hz
Young's double-slit interference is fundamental to our
understanding of the coherence properties of any wave
phenomenon. It has played a major role in the develop-
ment of optical coherence theory [I]. Double-slit interfer-
ence has also been observed with the de Broglie waves of
free electrons [2,3]. In this paper we describe an experi-
ment in which Rydberg wave packets are used to study
Young's double-slit interference within an atom. There
have been a number of experiments in recent years in
which a picosecond laser pulse is used to excite an elec-
tron into a linear combination of highly excited states in
the form of a spatially localized wave packet traveling
around a classical Kepler orbit [4,5]. Here we split one
electron into two separate wave packets and inject the two
packets into the opposite sides of a Rydberg-Kepler or-
bit. This is analogous to a Young s double-slit experiment
with the two slits on the opposite sides of the orbit, a dis-
tance of approximately one-half of a micron. By using
phase-locked laser pulses to excite the two wave packets
we can control the relative phase of the de Broglie wave
of the two packets. After the two packets have traveled
a number of times around the Kepler orbit, and each has
spread, the interference is quite dramatic with the relative
phase actually able to determine on which side of the orbit
a well-localized single-wave-packet revival occurs.
Although the analogy between our wave packet inter-
ferometer and Young's interferometer is not exact, it pro-
vides an intuition useful for interpreting our experiment
[6]. In Young's interferometer light is passed through an
opaque screen containing two slits. The two slits form
secondary light sources. The light from these secondary
sources is then allowed to propagate, and interference is
viewed on a distant screen. The best fringe visibility is
seen in the region where the light from the two sources
exactly overlaps spatially. The interferometer in our atom
is somewhat different. The wave packets are created by
two temporally separated laser pulses. The result is the
excitation of two spatially separated radial electron wave
packets which move around a common Kepler orbit. It
is the evolution of these two wave packets in the atomic
potential that eventually allows them to spread around the
entire orbit so they spatially overlap and interfere.
As a radial wave packet propagates around its orbit it
spreads due to the anharmonic nature of the atomic poten-
tial. The dynamics of the wave packet in this anharmonic
potential have been studied in detail by several authors
[7—12] (for an early review see Ref. [13]). They find that
the wave packet does not remain dispersed, but eventually
becomes relocalized, since it is a superposition of discrete
eigenstates. The time for the wave packet to relocalize
is called the revival time T~. At small integer ratios of
the revival time the wave packet can be well localized at
more than one radial position. It is during these "frac-
tional revivals" that the initially excited wave packet pair
can be maximally overlapped, and the best interference
fringe visibility can be seen.
The delay between the two laser pulses used to excite
the radial wave packets is precisely controlled to excite a
state that looks like a one-half fractional revival. The one-
half fractional revival is the form that a single-electron
wave packet takes when it has spread all of the way
around the orbit and interference between the head and
tail of the packet produces a fringe pattern in the form of
two miniature replicas of the original wave packet located
on opposites sides of the orbit [7,9,11,12]. The phase
relation between the pair of wave packets in the initial
fractional-revival-like state can be chosen arbitrarily. This
is in contrast with the fractional revival resulting from
the evolution of a wave packet excited by a single pulse
which has a specific phase between subwave packets. By
controlling this phase we can manipulate the interference
between the two wave packets, which occurs at a later
time. A third laser pulse is used to probe the evolution of
this superposition state and study the interference between
the two excited wave packets.
The use of phase coherent pulses to study radial wave
packets was first proposed a few years ago and has
since been used in several experiments [14—17]. In
these studies a single pump pulse is used. The pump
pulse excites a radial wave packet. This wave packet
is allowed to evolve for a given time. Next, a second
identical laser pulse is sent in to probe the wave packet
evolution. If the original wave packet is near the core it
can interact strongly with the probe pulse. The result of
1252 0031-9007/95/75(7)/1252(4)$06. 00 1995 The American Physical Society
VOLUME 75, NUMBER 7 PHYSICAL REVIEW LETTERS 14 AUt-vsT 1995
this interaction depends on the phase relationship between
the wave packet and the probe pulse as in a Ramsey
fringe experiment [18]. If the two are in phase more
population is coherently pumped into the excited state.
If the two are out of phase, the excited wave packet is
stimulated to make a transition back to the ground state
leaving no population in the excited state. When the
wave packet is not near the core the probe pulse does not
interact with the excited wave packet. By measuring the
excited state population after the probe-pulse interaction
we can determine the location of the wave packet. If large
oscillations at the optical period are seen in the population
(Ramsey fringes) then the wave packet was near the core
at the time of the probe pulse. No oscillation at the optical
period indicates the wave packet was not near the core
during the probe s interaction. This technique allows for
an excellent signal-to-noise ratio due to the efficiency with
which the excited state population can be measured using
simple dc field ionization.
In our experiment we use a Q-switched mode-locked
Nd: YAG laser to synchronously pump a dye laser. The
dye laser is cavity dumped at the Q-switch repetition rate
of 800 Hz to produce a 10 p, J laser pulse of 25 ps duration.
After frequency doubling, the pulse is sent into a series of
beam splitters, delay lines, and retroreflecting mirrors that
produce a train of three pulses (Fig. 1). Each is identical to
the first pulse, but with relative delays between the pulses
that are controlled to approximately one-hundredth of an
optical period. To achieve this degree of control, an active
servo stabilization system is used with a HeNe reference
laser. The three-pulse train is focused onto a potassium
atomic beam where the wave packets are excited. After
this interaction the excited state population is measured by
applying a dc electric field pulse, which ionizes all of the
population from the Rydberg series. The ions are collected
with an electron multiplier and counted for the various
configurations described below.
The experiment illustrated in Fig. 1 proceeds in two
parts. In the first part the motion of a single radial wave
packet is measured to serve as a calibration run. To do this,
the second pump pulse (label 2 in the diagram) is blocked
and the signal from the radial electron wave packet excited
by pulse 1 is measured with the phase sensitive pump-
probe technique. In our implementation of this technique
the delay between pulses 1 and 3 is scanned in two ways.
A corner cube mounted on a translation stage is used to take
coarse delay steps. At each of these coarse delays the servo
system is turned on and fine delay steps are taken with
the mirror mounted on the piezoelectric cylinder. This is
done by translating the detector, which is used in the fringe
stabilization circuit across the fringe pattern causing the
circuit to pull the fringes with it by moving the mirror in
arm 3. So, the raw data consist of a few Ramsey fringes at
each of the discrete coarse delay steps. The amplitude of
these fringes is a measure of where the radial wave packet
is in its evolution. Figure 2 shows the evolution of the
170
OO
cga
OQ
PZT
BS1 80
FIG. 1. Apparatus used to create a phase-coherent three-pulse
sequence. A single pulse from the dye laser enters from
the right of the figure, and the three-pulse train exits to the
top of the figure toward the atomic beam. The path length
difference between arms 1 and 2, and between arms 1 and 3
are independently interferometrically stabilized. This is done
by sending a reference beam from a HeNe laser into the
interferometer formed by arms 1 and 2. A piece of glass with
a small wedge is placed in the HeNe path in arm 1 to produce
tilt fringes at the output. A fringe stabilization circuit produces
an error signal from these tilt fringes which is fed back to the
piezoelectrically driven mirror in arm 2. An independent HeNe
beam and fringe stabilizer are used to control the path length
difference between arms 1 and 3.
(b)09.5 10 10.5 11
probe delay (T~)
11.5
FIG. 2. Radial wave packet evolution for excitation with a
single pump pulse. The laser frequency is tuned to excite a
wave packet near n = 66 in potassium. The Kepler period of
the orbit is Tz = 44 ps. The Ramsey fringe signal is shown
in (a) with a single fringe in the inset. The amplitude of eachof the Ramsey fringes is plotted in (b). At this delay time near
1the one-half fractional revival (2T~ = 11T~) the wave packet
is split into two pieces which pass the core at integer and half-
integer multiples of the Kepler period.
1253
VOLUME 75, NUMBER 7 PH YS ICAL REVIEW LETTERS 14 AUGUST 1995
wave packet near the one-half fractional revival. There
are peaks separated by half the Kepler period indicating
that the wave packet is localized at two spatial positions.
In the second part of the experiment we unblock the
second pump pulse and look at the interference between
two wave packets. (A similar type of wave packet
interference was considered by Alber, Ritsch, and Zoller
[8]. An interferometer within a molecule was described
by Garraway and Stenholm [19].) The delay between
the first and second pump pulses is set to one-half
of the Kepler period so that a state like the one-half
fractional revival is excited. The interference between
these two wave packets is investigated at a time near
one-half of the revival time. The reason for this choice
of probe time becomes obvious if we look at each wave
packet individually (Fig. 3). The first wave packet will
have evolved to the one-half fractional revival ~ The
two subwave packets of this state will pass the core at
integer and half-integer multiples of the Kepler period as
was described above. The wave packet produced by the
second pump pulse will also have evolved to the one-
half fractional revival state. Since the delay between the
two pump pulses was chosen to be one-half of the Kepler
period, each of the initially excited wave packets will have
evolved into states which exactly spatially overlap as they
pass the core near the one-half revival time. So, at this
probe time the wave packets excited by the individual
pump pulses can strongly interfere.
Figure 4 shows the evolution of a state excited with
the pair of phase coherent laser pulses for three particular
choices of phase difference. In the first case [Fig. 4(a)]
the phase was chosen so that the wave packets from the
two pump pulses which pass the core at integer multiples
of the Kepler period exactly cancel, and the packets
which pass the core at half-integer multiples of the Kepler
period add constructively. The result is a single well-
localized wave packet oscillating at the classical period:
a full revival. This phase was found experimentally by
fixing the probe delay at 10' and monitoring the Ramsey
fringe amplitude as the phase relationship between the two
pump pulses was varied. Once the fringe amplitude was
minimized, the phase between pump pulses was locked
and kept fixed as the delay of the probe pulse was scanned
to look at the wave packet evolution.
1 2 probe
)Lid
I
2 2 TR
1
l only 2 only
0
160
(a)
0—
TK12
O
4I8
C4
(I) = zi2 )':,
0
160
= -zi2
FIG. 3. (a) Time line for the laser pulse interaction. (b)
Cartoon plots of the radial probability distribution r2$2 of the
electron as a function of radius r The first column .(l only)
shows the evolution of the wave packet excited by pulse l
as if pulse 2 were not there. Column two shows the wave
packet evolution resulting from pulse 2 only. The third column
(1 + 2) shows the evolution resulting from the coherent sum of
the two wave packets. Near the half revival the localization
resulting from the coherent sum varies depending on the
exact phase relation between the wave packets. The resulting
localization for three particular choices of phase is shown.
1254
09.5
I
10 10.5 11
probe delay (Tz)
11.5
FIG. 4. Radial wave packet evolution for excitation with a
pair of phase coherent pump pulses. Probe delay is measured
from the first pump pulse and is in units of the Kepler period.
The phase between pump pulses modifies the interference seen
between the two wave packets near one-half of the revival time.
The phases are approximately (a) m. /2, (b) —vr/2, and (c) 7r
VOLUME 75, NUMBER 7 PHYSICAL REVIEW LETTERS 14 AUaUsT 1995
The next choice of phase [Fig. 4(b)] has a very similar
effect. Again, the wave packet is localized at one spatial
position at the probe time; however, now it passes the core
at integer multiples of the Kepler period. This is identical
to the behavior of a wave packet excited with a single
laser pulse and probed at a time near 2T~. Therefore the
pump pulse pair has excited the 3/2 fractional revival.
For the choice of phase in Fig. 4(c) the wave packet is
still split into two subpackets at the probe time. In fact,
for this case the wave packet will never come to a full
revival. Hence, this wave packet has no analog in a wave
packet excited by a single laser pulse.
The examples in Fig. 4 show the dramatic effect that a
simple change in phase can have on the future evolution
of a wave packet excited with this interferometric tech-
nique. For two special choices of phase the I/2 and 3/2
fractional revivals can be excited as shown in (a) and (b),
respectively. The phases for these two special cases dif-
fer by ~. This technique also allows for the excitation
of a fractional revival state with arbitrary phase between
subwave packets as in (c). It can be generalized further
by changing the coarse delay between pump pulses, look-
ing at other probe times, investigating higher order frac-
tional revivals, or interfering wave packets of two col-
ors. These examples illustrate via a generalization of the
Young's double-slit experiment that the coherence prop-
erties of atomic electron de Broglie waves dramatically
affect Rydberg wave packet evolution, and that by control
of the phase of these waves we can reproduce the interfer-
ence effects of classical optics.
We would like to acknowledge helpful discussions with
J. Bromage, Z. Gaeta, and M. Mallalieu. This work was
supported in part by the Army Research Ofhce.
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Young\u27s Double-Slit Interferometry within an Atom

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Young\u27s Double-Slit Interferometry within an Atom

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