Quantum Information Processing Based on Atomic Ensembles

1
Quantum Information Processing Based on Atomic
Ensembles
Guang-Can Guo
Key Laboratory of Quantum Information,
University of Science and Technology of China,
Hefei, 230026, PR China
2
Co-Workers
L. -M. Duan, Wei Jiang, Peng Xue, Chao Han,
Guo-Ping Guo
Outline
I. Introduction II. Quantum Repeaters with atomic
ensembles and linear optics III. Some
application in quantum information
processing with atomic ensembles IV.
Non-classical photon pairs generated from a
room- temperature atomic ensembles
3
I. Introduction
4
I. Introduction
The goal of quantum communication is to transmit
quantum states between distant sites. Such
transmission has potential application in the
secret transfer of classical messages by means of
quantum cryptography, and is also an essential
element in the construction of quantum networks.
5
I. Introduction
The basic problem of quantum communication is to
generate nearly perfect entangled states between
distant sites. All realistic schemes for quantum
communication at present are based on the use of
photonic channels. However, the degree of
entanglement generated between two distant sites
normally decreases exponentially with the length
of the connecting channels, because of optical
absorption and other channel noise.
6
I. Introduction
To regain a high degree of entanglement,
purification schemes can be used, but this does
not fully solve the long-distance communication
problem. Because of the exponential decay of the
entanglement in the channel, an exponentially
large number of partially entangled states are
needed to obtain one highly entangled state.
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I. Introduction
To overcome the difficulty associated with the
exponential fidelity decay, the concept of
quantum repeaters can be used. In principle, this
allows the overall communication fidelity to be
made very close to unity, with the communication
time growing only polynomial with transmission
distance.
8
I. Introduction
The proposed quantum repeater is a cascaded
entanglement-purification protocol for
communication system. The basic idea is to divide
the transmission channel into many segments, with
the length of each segment comparable to the
channel attenuation length.
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First, entanglement is generated and purified for
each segment The purified entanglement is then
extended to a greater length by connecting two
adjacent segments through entanglement
swapping. After this swapping, the overall
entanglement decreased, and has to be purified
again. The rounds of entaglement,swapping and
purification can be continued until nearly
perfect entangled states are created between two
distant sites.
I. Introduction
10
I. Introduction
Quantum memory is essential in the scheme of
quantum repeaters, because all purification
protocols are probabilistic. When entanglement
purification is performed for each segment of the
channel, quantum memory can be used to keep the
segment state if the purification succeeds, and
to repeat to purification for the segment only
where the previous attempt fails.
11
I. Introduction
This is essential for ensuring polynomial scaling
in the communication efficiency. Because if there
were no available memory, the purification for
all the segments would need to succeed at the
same time the probability of such an event
decreases exponentially with channel length.
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I. Introduction
The requirements of quantum memory means that we
need to store the local qubits in atomic internal
states. However, with atoms as the local
information carriers, it seems to be very hard to
implement quantum repeaters normally, one needs
to achieve the strong coupling between atoms and
photons by using high-finesse cavities for atomic
entanglement generation, purification, and
swapping, which remains a very challenging
technology.
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I. Introduction
Recently, Dr. Duan et al have proposed a
different scheme to realize quantum repeaters and
long-distance quantum communication with simple
physical setups. Let us introduce Duan's scheme.
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II. Quantum Repeaters with atomic ensembles and
linear optics
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II. Quantum Repeaters with atomic ensembles and
linear optics
Entanglement generation
The basic element of the system is a cloud of Na
identical atoms with the relevant level structure
show in the following figure
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II. Quantum Repeaters with atomic ensembles and
linear optics
All the atoms are initially prepared in the
ground state A sample is illuminated by a short,
off-resonant laser pulse that induces Raman
transitions into the state
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II. Quantum Repeaters with atomic ensembles and
linear optics
We are particularly interested in the
forward-scattered Stokes light that is
co-propagating with the laser. Such scattering
events are uniquely correlated with the
excitation of the symmetric collective atomic
mode S
where the summation is taken over all the atoms.
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II. Quantum Repeaters with atomic ensembles and
linear optics
In particular, an emission of the single Stokes
photon in a forward direction results in the
state of atomic ensemble given by
where the ensemble ground state
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II. Quantum Repeaters with atomic ensembles and
linear optics
Assume that the light-atom interaction time
is short, so that the mean photon number in the
forward-scattered Stokes pulse is much smaller
than 1. We can define an effective single-mode
bosonic operator a for this Stokes pulse with the
corresponding vacuum state denoted by
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II. Quantum Repeaters with atomic ensembles and
linear optics
The whole state of the atomic collective mode and
the forward-scattering Stokes mode can now be
written in the following form
where is the small excitation probability.
21
II. Quantum Repeaters with atomic ensembles and
linear optics
We note that a fraction of light is emitted in
other directions due to spontaneous emission. But
whenever Na is large, the contribution from the
spontaneous emission to the population in the
symmetric collective mode is small. As a result,
we have a large signal-to-noise ratio for the
process involving the collective mode. This ratio
is given by
where is the atom-field coupling constant,
is the natural line width of the
electronic excited state, k is the decay rate of
the photonic field mode in the cavity.
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II. Quantum Repeaters with atomic ensembles and
linear optics
In the case of the single-atom Na1, If we need
to get Rgt1, a high-Q microcavity is required.
The collective enhancement takes place because
the coherent forward scattering involves only one
collective atom mode S, whereas the spontaneous
emission distribute excitation over all atom
modes. Therefore only a small fraction of
spontaneous emission events influence the
symmetric mode S, which results in a large
signal-to-noise ratio.
23
II. Quantum Repeaters with atomic ensembles and
linear optics
Now we show how to use this setup to generate
entanglement between two distant ensembles L and
R.
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II. Quantum Repeaters with atomic ensembles and
linear optics
Here two laser pulses excite both ensembles at
same time, and the whole system is described by
the state , where is given
by
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II. Quantum Repeaters with atomic ensembles and
linear optics
The forward-scattered Stokes light from both
ensembles is combined at the beam splitter, and a
photon detector click in either D1 or D2 measures
the combined radiation from two samples, or
,Here denotes an unknown difference
of the phase shifts in the L and R side channels.
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II. Quantum Repeaters with atomic ensembles and
linear optics
Conditional on the detector click, we should
apply or to the whole state
, and projected state of the ensembles L and
R is nearly maximally entangled, with the form
27
II. Quantum Repeaters with atomic ensembles and
linear optics
The probability of getting a click is given by
for each round, so we need to repeat the process
about times for a successful entanglement
preparation and the average preparation time is
given by
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II. Quantum Repeaters with atomic ensembles and
linear optics
The presence of noise modifies the projected
state of the ensembles to
where the 'vacuum' coefficient is determined
by the dark count rates of the photon detectors.
It has been shown that any state in above
equation will be purified automatically to a
maximally entangled state in the
entanglement-based communication schemes.
Therefore we call this state an effective
maximally entangled (EME) state, with the vacuum
coefficient determing the purification
efficiency.
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II. Quantum Repeaters with atomic ensembles and
linear optics
Entanglement connection though swapping
After the successful generation of entanglement
within the attenuation length we want to extend
the quantum communication distance. This is done
by entanglement swapping show in figure above.
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II. Quantum Repeaters with atomic ensembles and
linear optics
We have two pair of ensembles, L and l1, l2 and R
distributed at three sites, L, l and R. Each of
the ensemble-pairs L and l1, l2 and R is prepared
in an EME state,
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II. Quantum Repeaters with atomic ensembles and
linear optics
The stored atomic excitation of two nearby
ensembles l1 and l2 are converted at the same
time into light. This is achieved by applying a
retrieval pulses of suitable polarization that is
near-resonant with the atomic transition
, which causes coherent conversion of atomic
excitation into photons that have a different
polarization and frequently to retrieval pulse.
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II. Quantum Repeaters with atomic ensembles and
linear optics
The efficiency of this transfer can be very close
to unity even at a single quantum level due to
collective enhancement.
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II. Quantum Repeaters with atomic ensembles and
linear optics
After the transfer, the stimulated optical
excitations interfere at a 50-50 beam splitter,
and then detected by the single-photon detectors
D1 and D2. If either D1 or D2 clicks, the
protocol is successful and an EME state is
established between the ensembles L and R with a
double communication distance.
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II. Quantum Repeaters with atomic ensembles and
linear optics
Otherwise, the process fails, and we need to
repeat the above entanglement generation and
swapping until finally we have a click in D1 or
D2, that is, until the protocol finally succeeds.
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II. Quantum Repeaters with atomic ensembles and
linear optics
The above method for connecting entanglement can
be cascaded to arbitrarily extend the
communication distance. Assume that we want to
communicate over a distance LLn2nL0. By fixing
the overall fidelity imperfection to be a desired
small value , the total communication time
scales with distance by the law where the
success probabilities pi, pa for the i th
entanglement connection and for the entanglement
application. is overall efficiency of the
entangle generation.
36
III. Some application in quantum information
processing with atomic ensembles
37
III. Some application in quantum information
processing with atomic ensembles
1. Scheme for preparation of multipartite
entanglement of atomic ensembles
We know that the entanglement of the W state is
maximally robust. For example, the W state for
three qubits is as
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III. Some application in quantum information
processing with atomic ensembles
If we lose any one of these three qubits, the
remaining reduced density matrices retain the
entanglement between other qubits. So W state has
some useful application in quantum information,
such as controlled quantum teleportation. Now how
to prepare the W class of entangled state in
experiments?
39
III. Some application in quantum information
processing with atomic ensembles
Here we describe an experimental scheme of
preparing multipartite W class of maximal
entanglement between atomic ensembles in the
following figure
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III. Some application in quantum information
processing with atomic ensembles
(1) The first step is to share an EPR type of
entangled state between two distant ensembles 1
and 2 using the above way.
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III. Some application in quantum information
processing with atomic ensembles
(2) Then connect the other two distant ensembles
2 and 3. The ensemble 3 is prepared in the ground
state first. So the whole system is described
by the state . We use two pumping
pulse to excide ensembles 2 and 3 at the same
time. The forward-scattering Stokes light from
both ensembles is combined at 50-50 beam splitter
after some filters that filter out the pumping
laser pulses.
42
III. Some application in quantum information
processing with atomic ensembles
If one photon is detected by either of the
detector D1 or D2, we get state Otherwise, we
need to manipulate repumping pulses to the
transition on the three ensembles
and set them back to the ground state , then
repeat step 1 and 2 until finally we get a click
in either of the two detectors.
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III. Some application in quantum information
processing with atomic ensembles
(3) A repumping laser pulse is applied to the
ensemble 2. If one excitation is registered
from it, we succeed and go on with the next step.
At this step, we can get state
44
III. Some application in quantum information
processing with atomic ensembles
(4) However does not belong to the W
class of maximally entangled states. So then we
connect ensembles 1 and 3 using the same way as
in step (2), and apply a repumping laser pulse to
the ensemble 1, after a click in D4 or D5. If
there is one excitation registered by D6, we get
W state By the same way we can entangle n
ensembles in the W state.
45
III. Some application in quantum information
processing with atomic ensembles
2. Entanglement of individual photon and
atomic ensembles
We know that in most of the previous protocols
the entangled subsystems are congener (the same
kind of objects). In the novel quantum
information theory, individual photon becomes a
perfect chosen for flying qubit. On the other
hand, atomic ensemble has enabled it as a well
candidate for stationary and register qubits of
quantum information and computation.
46
III. Some application in quantum information
processing with atomic ensembles
Here we present an idea to entangle an individual
photon and atomic ensemble to integrate the
features of both flying qubit and stationary
qubit.
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III. Some application in quantum information
processing with atomic ensembles
Two identical atomic samples are placed in a
beeline with a half wave plate and a polarization
beam splitter plate (PBS) between them. Using
above way we can induces atom Raman transition.
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III. Some application in quantum information
processing with atomic ensembles
What particularly interests us is the
forward-scattered Stokes light. Assume the Stokes
photon from the emission is right-handed
rotation, and we define an effective single-mode
bosonic operator for this Stokes. The plate
between the two samples is employed to transform
this Stokes photon into left-handed rotation. Its
function can be denoted by operator
L, R -- left, right handed rotation
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III. Some application in quantum information
processing with atomic ensembles
In the case there is only one Stokes photon, the
whole system of the two atomic ensembles and the
photon can be written in state
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III. Some application in quantum information
processing with atomic ensembles
We can adjust two parameters , to alter
the entanglement degree of the above state with
linear optics such as the polarization beam
splitter plate placed between the two atomic
ensembles.
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III. Some application in quantum information
processing with atomic ensembles
This polarization plate controls the pass ratio
of the Left-handed rotation Stokes photon from
the first atomic ensemble. Finally the Stokes
photons pass through a plate which
transforms the circularly - polarized wave to the
linearly polarized light. Thus becomes
the maximally entangled EPM state
The subsystem of the entanglement are different
species, individual photons and atomic ensembles.
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III. Some application in quantum information
processing with atomic ensembles
This Stokes photon p and the addition photon A or
q interfere at a 50-50 beam splitter BS, with the
outputs analyzed by two double-channel polarizer
respectively and detected by four single-photon
detectors DH, DV', Dv and DH'. In fact, this is a
Bell-state analyzer. The coincidence clicks
between DH and DV' or DV and DH corresponds
and coincidence clicks betweenDH and DV or
DV and DHcorresponds .
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III. Some application in quantum information
processing with atomic ensembles
As no post selection is needed, this event-ready
entangled state between stationary and flying
qubits can be straightforwardly applied in
various quantum information processing. For
example, this entangled state can be explored as
a valuable individual photons quantum memory.
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III. Some application in quantum information
processing with atomic ensembles
Here is a reversible quantum memory scheme for
individual polarization photons which is well
based on the atomic ensemble anti-Raman process.
As there is no random for the generation of
anti-Stokes photon, no photon non-demolition
measurement device is required in the present
quantum memory protocol.
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III. Some application in quantum information
processing with atomic ensembles
The quantum memory can be divided into three
stage
(1) Initial preparation of the memory Two pair of
ensembles , have been
prepared into EME states by Raman process
These four atomic ensembles in above state form
the quantum memory for individual polarization
photon.
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III. Some application in quantum information
processing with atomic ensembles
(2) Storage of a single photon polarization state
conditioned to a Bell measurement When the
polarization photon needed recording comes, we
anti-pump the ensembles A1 and B1 in turn to
transfer their excitation mode to the anti-Stokes
photon polarization mode . This
forward-scattering anti-Stokes photon and the
incoming photon are then measured with a Bell
state analyzer.
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III. Some application in quantum information
processing with atomic ensembles
At this state, the state is After the
operation of the Bell state analyzer, the state
of the incoming photon is teleported to atomic
ensembles with a probability of .
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III. Some application in quantum information
processing with atomic ensembles
(3) Manipulation and read out of this state As
the atomic ensembles collective excited mode can
be effortlessly transferred to photon modes, the
stored quantum information can be efficiently
manipulated and readout in the present
reversible quantum memory.
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IV. Non-classical photon pairs generation from a
room-temperature atomic ensemble
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IV. Non-classical photon pairs generation from a
room-temperature atomic ensemble
The important step for quantum repeaters and
above schemes of application is to demonstrate
quantum correlation between the emitted
single-photon and the long-lived collective
atomic excitation. Here we show our experiment to
realize this important step by observing
non-classical correlation between them in a
room-temperature atomic vapor. The collective
atomic excitation is transferred subsequently to
a photon in experiment, so actually we observe
non-classical correlation between two
successively emitted photons.
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IV. Non-classical photon pairs generation from a
room-temperature atomic ensemble
(a)
SM fiber
(b)
write
Anti-Stokes photon
read
Stokes photon
(c)
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IV. Non-classical photon pairs generation from a
room-temperature atomic ensemble
The write and the read pulses are from two
different semiconductor laser working at a
wavelength about 795nm. After the cell, we need
to separate the weak signal of Stokes or
anti-Stokes photons from the strong write and
read laser pulses. This is done by both
polarization and frequency (PBS2, F1, F2).
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IV. Non-classical photon pairs generation from a
room-temperature atomic ensemble
After the filter, both of the Stokes and
anti-Stokes photons are split by a 50-50 beam
splitter, and then coupled into single-mode
fibers, which direct them to the four single
photon detectors. With this setup, we can measure
both the auto-correlation and cross-correlation
between the Stokes and the anti-Stokes photons.
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IV. Non-classical photon pairs generation from a
room-temperature atomic ensemble
First, the write pulse includes Stokes photon
which are detected by the signal photon detectors
DA and DB. After a controllable time delay
, we send the read pulse, through the atomic
ensemble. This read pulse transfers the
collective atomic excitation back to anti-Strokes
photons which are detected by DC and DD.
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IV. Non-classical photon pairs generation from a
room-temperature atomic ensemble
Then from the coincidence between them, we can
get the auto-correlation
and the cross-correlation
From the results, we can confirm the
non-classical correlation between the Stokes and
the anti-Stokes fields. As the anti-Strokes field
is transferred from the collective atomic mode,
this also confirms the non-classical correlation
between the collective atomic mode and the
forward propagating Stokes mode.
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IV. Non-classical photon pairs generation from a
room-temperature atomic ensemble
To confirm the non-classical feature of the
correlation between the Stokes and the
anti-Stokes field, we make use of the
Cauchy-Schwarz inequality The auto and cross
correlation function between the Stokes field 1
and anti-Stokes field 2 can be directly obtained
from the measured coincidence rates.
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IV. Non-classical photon pairs generation from a
room-temperature atomic ensemble
In our experiment, the results are
So the Cauchy-Schwarz inequality is manifestly
violated by our experiment.
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IV. Non-classical photon pairs generation from a
room-temperature atomic ensemble
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IV. Non-classical photon pairs generation from a
room-temperature atomic ensemble
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IV. Non-classical photon pairs generation from a
room-temperature atomic ensemble
72
IV. Non-classical photon pairs generation from a
room-temperature atomic ensemble
Compared with two other experiments recently
(Kimble and Luckin), our experiment is
distinctive by the following features
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IV. Non-classical photon pairs generation from a
room-temperature atomic ensemble
We observe non-classical correlation between
photon pairs generated from a room-temperature
atomic vapor cell. Kimble et al used cold atom.
So, our setup is much cheaper. Luckin et al based
on an atomic vapor cell, however, it is not
performed in the single-photon region.
(1)
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IV. Non-classical photon pairs generation from a
room-temperature atomic ensemble
In our experiment, we demonstrate a time delay of
2 microsecond between the pair of non-classical
correlated photons which is considerably longer
than the 400-nanosecond time delay reported by
Kimble et al.
(2)
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Thank you very much!