λ
(nm)
879.5
879.7
879.9
Transmission (a.u.)
0
1
GHz
0
50
-50
-100
100
experiment
2 Gaussian theory
1 Gaussian theory
Supplementary Figure
1.
Experimental and theoretical on-resonance spectrum in a
0.1% Nd:YVO cavity
Black curve is the experimental spectrum. Red curve is the theoretical
spectrum using a model based on two distinct Gaussian sub-ensembles, which reveals a middle
peak that is consistent with the experiment. Blue dotted curve is the theoretical spectrum using
a model based on one Gaussian distribution whose inhomogeneous width approximates the total
width of the two Gaussian sub-ensembles. The blue curve does not show the middle peak, but
otherwise coincides with the red curve well.
1
Count (a.u.)
0
1
τ (ps)
Counts (a.u.)
0
1
Counts (a.u.)
0
1
a
b
c
Theory
Experiment
τ
R
2τ
R
single polariton
two polaritons
detuned cavity
y
0
20
40
60
80
τ (ps)
0
20
40
60
80
τ=31.8 ps
τ=29.8 ps
3τ
R
4τ
R
5τ
R
Supplementary Figure
2.
Time-domain interferometric measurements of the 1%
Nd:YVO cavity transmission.
Left panels show the cavity transmission spectra for the two
pulses under different excitation schemes. Grey area is for uncoupled cavity; red for excited po-
lariton states. The colored areas were plotted against the polariton spectrum (solid curve).
a,
Simulated and measured cavity decay (i.e. lifetime) when uncoupled from the atoms.
b,
Decay of
singly excited lower (upper) polarition.
c,
Decayed oscillations when both polaritons were excited
with transform-limited pulses. The dotted grey and red curves are single exponential fit to the
decaying amplitude of the fringe signal, from which the decay time constants are extracted.
2
Detuning (GHz)
300
200
100
0
-100
-200
-300
Γ (GHz)
20
30
40
50
60
70
80
90
100
Detuning (GHz)
80
60
40
20
0
-20 -40 -60 -80
Γ (GHz)
20
25
30
35
40
45
50
upper polariton
lower polariton
upper polariton
lower polariton
a
b
1% Nd:YVO
0.1% Nd:YVO
(nm)
879.3 879.6 879.9 880.2
scan time (a.u.)
60
80
100
120
140
160
180
200
220
240
0
1000
2000
3000
4000
5000
λ
1% Nd:YVO
λ (nm)
879.4
879.6
879.8
880
scan time (a.u.)
40
60
80
100
120
140
160
180
200
220
0
500
1000
1500
2000
0.1% Nd:YVO
optical intensity
optical intensity
Supplementary Figure
3.
Experimental polariton linewidths versus detuning. a,
1%
Nd:YVO.
b,
0.1% Nd:YVO. Black (dark blue) triangles are for lower (upper) polariton. Green
curves are theoretical linewidths for both polaritons assuming a Lorentzian ensemble distribution.
3
Supplementary Note 1. Theoretical decay rates of a coupled cavity-ensemble system
The cavity-ensemble coupled system is described by the Tavis-Cummings Hamiltonian.
We model the system following [1], which consists of a cavity mode
a
of frequency
ω
0
coupled
with strength
g
k
to a distribution of
N
two-level emitters described by modes
b
k
. We define
the cavity frequency
ω
0
and the frequency of each emitter as
ω
k
. We account for the atomic
dephasing rate (homogeneous linewidth)
γ
h
and label the cavity intensity decay as
κ
. Using
the standard input-output formalism for a two sided cavity with input field
c
in
, reflected
field
c
r
, and transmitted field
c
t
gives the Heisenberg equations for the system:
̇
a
=
−
[
κ
2
+
i
(
ω
0
−
ω
)
]
a
−
√
κ
2
c
in
+
∑
k
g
k
b
k
̇
b
k
=
−
[
γ
h
2
+
i
(
ω
k
−
ω
)
]
b
k
−
g
k
a
c
t
=
√
κ
2
a
c
r
=
c
in
+
√
κ
2
a.
(1)
By solving this set of equations in the steady state, we arrive at the complex transmission
of the cavity:
t
(
ω
) =
〈
c
t
〉
〈
c
in
〉
=
−
κ
2
i
ω
0
−
iκ
2
−
ω
−
∑
k
g
2
k
ω
k
−
iγ
h
2
−
ω
.
(2)
For a large number of emitters, we can define the distribution of emitters in terms of a
continuous spectral density
ρ
(
ω
) =
∑
k
g
2
k
δ
(
ω
−
ω
k
)
Ω
2
.
Here Ω is the collective coupling strength
defined by Ω
2
=
∑
k
g
2
k
. The continuum form of the transmission is then [1]
t
(
ω
) =
−
κ
2
i
ω
0
−
iκ
2
−
ω
+ Ω
2
∫
ρ
(
ω
′
)
dω
′
ω
−
ω
′
+
iγ
h
2
.
(3)
Lorentzian distribution
In the case of a Lorentzian distribution,
ρ
(
ω
) =
∆
π
1
∆
2
+(
ω
−
ω
a
)
2
,
where 2∆ is the FWHM of the inhomogeneous linewidth and
ω
a
denotes the center frequency
of the ensemble, Eq. (3) is integrable to
t
(
ω
)
Lorentzian
=
−
κ
2
i
ω
0
−
iκ
2
−
ω
+
Ω
2
ω
−
ω
a
+
iγ
h
/
2+
i
∆
.
(4)
The poles of the transmission function yield
ω
±
=
ω
a
+
δ/
2
−
i
κ
+
γ
h
+ 2∆
4
±
√
Ω
2
+ [(
iκ
−
2
i
∆
−
iγ
h
−
2
δ
)
/
4]
2
,
(5)
4
where we define the cavity-ensemble detuning as
δ
=
ω
0
−
ω
a
. Eq. (5) determines the
locations and linewidths of the two polariton modes:
Γ
±
=
κ
+
γ
h
+ 2∆
2
±
Im(
√
4Ω
2
+ [(
iκ
−
2
i
∆
−
iγ
h
−
2
δ
)
/
2]
2
)
,
(6)
which checks Γ =
κ
+
γ
h
+2∆
2
for the on-resonance (
δ
=0), strong coupling (Ω
κ,
∆) condi-
tion. The green curves in Fig. 2
c
,2
f
are thereby evaluated from Eq. (6).
Gaussian distribution
In the case of a Gaussian distribution,
ρ
(
ω
) =
1
∆
√
π
e
−
(
ω
−
ω
a
)
2
/
∆
2
.
Note that the definition of ∆ here is different from that in [1]. We define ∆ such that the
FWHM of the Gaussian distribution is 2
√
ln2∆, which is consistent with the q-Gaussian
definition in the text. Integrating Eq. (2) gives
t
(
ω,δ
)
Gaussian
=
−
κ
2
i
ω
a
+
δ
−
iκ
2
−
ω
−
i
Ω
2
∆
√
πe
−
(
ω
−
ω
a
+
iγ
h
/
2
∆
)
2
erfc(
−
i
ω
−
ω
a
+
iγ
h
/
2
∆
)
.
(7)
where erfc is the complex complementary error function. There is no straightforward ana-
lytical solution for the poles of the transmission function. Therefore we numerically solve
for the transmission poles and the polariton linewidth as a function of the cavity-ensemble
detuning
δ
.
To plot the theoretical decay rates in Fig. 2
c
,2
f
, we need experimental values for
κ
, ∆,
Ω and
γ
h
. In the case of a far detuned cavity, using a spectrometer (with resolution of 4
GHz) we directly measured
κ
= 2
π
×
44 GHz for the 0.1% Nd:YVO device, and
κ
= 2
π
×
20
GHz for the 1% Nd:YVO device. As discussed in the main text, the atomic distributions
are approximately Gaussian, with ∆
/
2
π
=14.6 GHz from fitting the two branches with
one Gaussian for the 0.1% Nd:YVO device, and a ∆
/
2
π
=45.6 GHz for the 1% Nd:YVO
device. We then measured
γ
h
/
2
π
=1/
π
T
2
= 0.82 MHz for 0.1% Nd:YVO using two-pulse
photon echoes. We could not measure any echo signal from the 1% Nd:YVO device, which
is probably due to significant ion-ion interactions in a highly doped sample. However, we
estimated an upper bound of
γ
h
/
2
π
≤
40MHz by transient hole burning in the 1% sample.
To determine Ω, we fit the on-resonance transmission spectra (Fig. 2
b,e
) with Ω as the
only free parameter. Fitting based on Eq. (7) allows us to determine the collective coupling
strength Ω = 2
π
×
25 GHz for the 0.1% device, and Ω = 2
π
×
55 GHz for the 1% device.
Supplementary Note 2. Explanation of the middle peak in 0.1% Nd:YVO nanocavity
When tuning the cavity across the Nd Y
1
-Z
1
transition in the 0.1% device, we observed
a weak transmission peak between the two polariton modes. This peak is caused by cou-
5
pling a cavity to two distinct ensembles of emitters spectrally separated by 2
δ
a
, which was
theoretically predicted and analysed in Section VI. B of [1]. This middle peak corresponds
to the eigenstate resulting from the coupling between the cavity mode and the antisymmet-
ric state
|
A
〉
= (
|
G
1
,S
2
〉−|
S
1
,G
2
〉
)
/
√
2, where
G
j
,S
j
are ground and excited state of the
superadiance collective state of
j
th ensemble. According to [1], the state giving rise to the
middle peak is written as
iδ
a
|
1
,G
1
,G
2
〉
+ Ω
√
2
|
0
,A
〉
. This state would be completely dark
if Ω
δ
a
, and has a small cavity component otherwise, which we show below is the case in
our 0.1% Nd:YVO device.
To model the system, we start with a atomic distribution as a summation of two Gaussian
distributions spectrally separated by 2
δ
a
:
ρ
(
ω
) =
1
2∆
√
π
e
−
(
ω
−
ω
a
−
δ
a
)
2
/
∆
2
+
1
2∆
√
π
e
−
(
ω
−
ω
a
+
δ
a
)
2
/
∆
2
.
Each Gaussian subensemble is one Zeeman branch and consists of half of the total popula-
tion due to a thermal distribution at 3.6 K. The on-resonance (
δ
= 0) cavity transmission
spectrum can be obtained by evaluating Eq. (3), which modifies Eq. (7) to
t
(
ω
) =
−
κ
2
i
ω
a
−
iκ
2
−
ω
−
i
Ω
2
2∆
√
π
∑
j
=1
,
2
e
−
(
ω
−
ω
aj
+
iγ
h
/
2
∆
)
2
erfc(
−
i
ω
−
ω
aj
+
iγ
h
/
2
∆
)
.
(8)
where
ω
a
1
=
ω
a
−
δ
a
,
ω
a
2
=
ω
a
+
δ
a
are the central frequencies of two Zeeman branches,
respectively.
From the absorption spectrum in Fig. 1
b
for 0.1% Nd:YVO, we extract the parameters
δ
a
=8.5 GHz, and ∆ =5.0 GHz. With
κ
and
γ
h
measured above, we plot in Fig. 2
e
and
Supplementary Figure 1 the theoretical transmission (red curve) based on Eq. (8). Note
that this theoretical curve is not a fit, which clearly reveals the middle peak. The measured
transmission spectrum is overlaid with the theory curve, showing good agreement.
In Fig. 2f of the main text, the polariton decay Γ was compared to the expected decay
from a Gaussian ensemble that has the same FWHM as the sum of the two Zeeman branches
combined. Here we justify that this approximation of two Zeeman sub-ensembles by one
broader Gaussian distribution is valid. As mentioned in the main text, to treat the entire
ensemble as one Gaussian distribution, we find the effective FWHM to be 24 GHz, and
∆
/
2
π
=14.6 GHz. We plot the expected on resonance transmission using Eq. (7) in blue in
Supplementary Figure 1. We see a high degree of agreement between the red and blue curves
except for the middle peak region. This means the one-Gaussian approximation captures
all the essential properties of the polariton spectrum. This is expected from the conclusions
6
drawn from [1], that the polariton linewidths only depend on the profile of the tails of the
distribution, but not the central region of the distribution function
ρ
(
ω
). Thus we confirm
the validity of the one-Gaussian approximation.
Supplementary Note 3. Experimental polariton linewidths versus detuning
Here we plot the linewidths of both upper (shorter wavelength) and lower (longer wave-
length) polaritons as the cavity was tuned from shorter to longer wavelengths across the
atomic transition. For 1% Nd:YVO, the evolution of each polariton linewidth with detuning
is asymmetric about the ensemble center frequency (Supplementary Figure 2a). Two peaks
at 50 GHz, and -160 GHz detuning are evident. We believe these two peaks are due to
cavity coupling to two satellite lines of the main transition. Given the high density of this
sample, we expect that these satellite lines correspond to the Nd-Nd pair site (resulting from
Dzyaloshisky-Moriya interactions), which were measured to be +48 GHz and -166 GHz de-
tuned from the line center [2]. On the other hand, in 0.1% Nd:YVO (Supplementary Figure
2b), the linewidths of upper and lower polaritons as a function of detuning appear to be
symmetric. This is expected from the symmetric shape of the ensemble distribution (Fig.
1b in the main text), and the absence of strong pair-site satellite lines at this lower doping
concentration. Again, we plot in dark green the theoretical linewidths of the polaritons for
the case of a Lorentzian distribution. At zero detuning, the linewidths of both polaritons
should converge to a value
κ/
2 +
γ
h
/
2 + ∆ (i.e. the Lorentzian limit with no protection
effect). In Supplementary Figure 2a, 2b, the gap between the experimental zero-detuning
(on-resonance) linewidths and the Lorentzian limit represents the amount of linewidth nar-
rowing and the extent of cavity protection. This narrowing is highlighted by a red arrow.
Supplementary Note 4. Simulation of the dynamics of the coupled system
To simulate the temporal dynamics of the system (Fig. 3 theoretical plots and Fig. 4b), we
start from the discrete form of the differential equations Eq. (1). In this case, simulating the
entire system of
N
emitters entails solving a set of
N
∼
10
6
coupled differential equations. To
make the problem more computationally tractable, we instead solve the system of
N
sim
N
coupled emitters with their frequencies randomly assigned according to the experimentally
7
measured atomic distribution
ρ
(
ω
). The coupling strength of each emitter is set as
g
=
Ω
/
√
N
sim
such that the collective coupling strength is held constant at the experimental value
Ω =25 GHz. This reduced set of equations was then solved numerically in Mathematica using
the built-in differential equation solver (NDSolve). The number of simulated emitters was
increased until the solution converged (i.e. until increasing the number of simulated emitters
no longer had an effect on the solution). All emitters were assumed to start in the ground
state in an empty cavity. The cavity and probe were assumed to be on resonance with the
center of the emitter spectral distribution. The input field consisted of two 4(1.5) ps pulses
for 0.1% (1%) doped cavity separated by variable time
τ
. The amplitude of the integrated
interference (corresponding to the measurement) for each value of
τ
was determined by
integrating the cavity transmission over the simulation time (10 cavity lifetimes).
Supplementary Note 5. Relationship between the decay time constants of the inter-
ferometric signal and the polariton linewidth
The experiments we performed to obtain Fig. 3 are optical field autocorrelation measure-
ments at the single photon level. Here we clarify how the decay times of the interferometric
signals (Fig. 3 right panel) are related to the actual polariton decay times. Given a polariton
linewidth Γ, the 1
/e
intensity decay constant is 1
/
Γ [3]. The field decay constant would be
twice as long 2
/
Γ. The interference of two identical but time-delayed field generates an
autocorrelation function of the field. In our case, the field is exponentially decaying in time.
The autocorrelation of an exponential decay function is another exponential decay with
twice the decay constant. Therefore, the interference signal should yield a decay constant
4
/
Γ. We verify this relationship experimentally by measuring the decay time of an empty
(far-detuned) cavity. For 0.1% Nd:YVO cavity,
κ
= 2
π
×
44 GHz, thus the cavity lifetime is
1
/κ
=3.6 ps. By using the optical autocorrelation technique, we measured a decay constant
of the interference signal to be 14.5 ps, as shown in blue-dotted fit in Fig. 3
a
, which is equal
to 4
/κ
.
8
Supplementary Note 6. Temporal measurements of the cavity transmission for 1%
Nd:YVO device
Supplementary Figure 3 plots the theoretical interference fringe amplitudes along with the
measured results. The mean photon number per pulse coupled in the cavity was estimated to
be
μ
=0.5. The case of an uncoupled cavity is plotted in Supplementary Figure 3a, showing
a fitted decay constant (4
/κ
) of
∼
31.8 ps. When only one polariton (
|
0
〉
or
|
1
〉
) was excited,
the decay was 29.8 ps (Supplementary Figure 3b). For the superposition of two polaritons,
Ramsey-like fringes were obtained, revealing at least 5 Rabi oscillations (Supplementary
Figure 3c). The dotted blue and red curves are single exponential fits to the decaying
amplitude of the fringe signal.
Supplementary Note 7. Construction of qubit density matrix from interference fringes
of two photons
The state of an arbitrary qubit
|
ψ
〉
=
α
|
0
〉
+
β
|
1
〉
, where
|
α
|
2
+
|
β
|
2
= 1, can be determined by
taking a set of four projection measurements represented by the operators ˆ
μ
0
=
|
0
〉〈
0
|
+
|
1
〉〈
1
|
,
ˆ
μ
1
=
|
+
〉〈
+
|
, ˆ
μ
2
=
|
〉〈
|
, ˆ
μ
3
=
|
0
〉〈
0
|
[4]. The outcome of these measurements are
n
j
=
C
Tr
{
ˆ
ρ
ˆ
μ
j
}
,
(9)
where
ρ
=
|
φ
〉〈
φ
|
for a pure state and the scaling factor
C
is the number of detected photons,
which will be set to 1 in the following derivation. We explicitly write out the four
n
j
values
for an arbitrary qubit as
n
0
= 0
.
5(
|
α
|
2
+
|
β
|
2
) = 0
.
5
n
1
= 0
.
5
|
α
+
β
|
2
n
2
= 0
.
5
|
α
−
iβ
|
2
n
3
=
|
α
|
2
.
(10)
9
From these values, the four Stokes parameters are calculated as
S
0
= 2
n
0
S
1
= 2(
n
1
−
n
0
)
S
2
= 2(
n
2
−
n
0
)
S
3
= 2(
n
3
−
n
0
)
.
(11)
The density matrix ˆ
ρ
is then constructed from the Stokes parameters by
ˆ
ρ
=
1
2
3
∑
j
=0
S
j
S
0
ˆ
σ
j
,
(12)
where ˆ
σ
0
is the identity operator
ˆ
I
and ˆ
σ
1
,
2
,
3
are the Pauli spin operators.
Now we turn to the measurement of interference between two photonic states represented
by the electric field operators
ˆ
E
1
(
t
) =
α
1
e
−
iω
−
t
a
−
+
β
1
e
−
iω
+
t
a
+
and
ˆ
E
2
(
t
) =
α
2
e
−
iω
−
t
a
−
+
β
2
e
−
iω
+
t
a
+
, where
ω
−
,
ω
+
are the optical frequencies of the lower and upper polaritons,
respectively, with frequency difference
ω
+
−
ω
−
= Ω
R
. For simplicity, we do not include
the finite linewidth of each polariton as it does not affect the results of the tomography
measurement. The field operator at the single photon detector is
ˆ
E
(
t
) =
ˆ
E
1
(
t
−
τ
R
) +
ˆ
E
2
(
t
)
corresponding to the first photon delayed by
τ
R
after storage in the ensemble. The count
rate on the detector is
C
∝〈
E
(
t
)
†
E
(
t
)
〉
= 2 + 2 cos
φ
|
α
1
α
∗
2
+
β
1
β
∗
2
e
−
i
Ω
R
τ
R
|
= 2 + 2 cos
φ
|
α
1
α
∗
2
+
β
1
β
∗
2
|
,
(13)
where the last equality holds for Ω
R
τ
R
= 2
π
. Here
φ
is the carrier phase difference between
the two photons, which is varied from 0 to 2
π
to produce interference fringes with a peak-to-
peak amplitude
C
max
−
C
min
= 4
|
α
1
α
∗
2
+
β
1
β
∗
2
|
. We define a set of experimentally measurable
fringe amplitude parameters
A
=
C
0
|
α
1
α
∗
2
+
β
1
β
∗
2
|
, where
C
0
is a constant factor representing
the integrated counts. These parameters closely resemble the projection measurement out-
comes in Eq. (10) (different by a power of 2) depending on the states encoded on the second
photon, i.e.
α
2
|
0
〉
+
β
2
|
1
〉
. For instance, if we encode the second photon in the same qubit as
the first photon but attenuate the intensity by a factor of 2 , i.e.
α
2
=
α
1
/
√
2,
β
2
=
β
1
/
√
2,
we get the amplitude
A
0
=
C
0
√
2
(
|
α
1
|
2
+
|
β
1
|
2
). For
α
2
=
β
2
= 1
/
√
2,
A
1
=
C
0
/
√
2
|
α
1
+
β
1
|
.
For
α
2
=
−
iβ
2
= 1
/
√
2,
A
2
=
C
0
/
√
2
|
α
1
−
iβ
1
|
. For
α
2
= 1,
β
2
= 0,
A
3
=
C
0
|
α
1
|
. Based on
10
the four amplitude values, we construct an equivalent set of Stokes parameter
S
A
j
S
A
0
= 2
A
2
0
S
A
1
= 2
A
2
1
−
2
A
2
0
S
A
2
= 2
A
2
2
−
2
A
2
0
S
A
3
= 2
A
2
3
−
2
A
2
0
,
(14)
from which the density matrix is calculated by
ˆ
ρ
=
1
2
3
∑
j
=0
S
A
j
S
A
0
ˆ
σ
j
=
1
2
[
ˆ
I
+
(
(
A
1
/A
0
)
2
−
1
)
ˆ
σ
1
+
(
(
A
2
/A
0
)
2
−
1
)
ˆ
σ
2
+
(
(
A
3
/A
0
)
2
−
1
)
ˆ
σ
3
]
.
(15)
Then we perform a maximal likelyhood estimation [4] to obtain a physical density matrix,
which is used to calculate the fidelity
F
=
〈
ψ
in
|
ˆ
ρ
|
ψ
in
〉
Supplementary Note 8. Classical storage fidelity for weak coherent photons
The classical fidelity for any storage device measures the best input/output fidelity one can
achieve using a classical method. For a given photon number of the input state
N
ph
, the
maximum classical fidelity is known to be
F
=
N
ph
+1
N
ph
+2
[5]. For an input pulse that is in a
coherent state with a mean photon number
μ
, the Poissonian statistics give a
N
-photon
probablity of
P
(
N
ph
) =
e
−
μ
μ
N
ph
N
ph
!
. Accounting for each
N
-photon component, the classical
fidelity of a coherent state is then
F
=
∞
∑
N
ph
≥
1
N
ph
+ 1
N
ph
+ 2
P
(
N
ph
)
1
−
P
(0)
(16)
In addition, for an imperfect memory with storage and retrieval efficiency
η <
1, the classical
fidelity would be higher because a classical memory can preferentially measure the higher
photon component of the input and send out a new qubit. We follow the strategy in [6, 7]
that there exists a threshold photon number
N
min
that the classical memory sends out a qubit
when the input photon number is greater than this value, which happens with a probability
1
−
p
. Otherwise the memory sends out a result for input photon
N
min
with probability
p
.
Combing the two cases, the memory efficiency is expressed as
η
=
p
+
∑
N
ph
≥
N
min+1
P
(
N
ph
)
1
−
P
(0)
(17)
11
For a given
μ
and
η
, the value of
N
min
can be readily calculated according to [7],
N
min
= min
i
:
∑
N
ph
≥
i
+1
P
(
N
ph
)
≤
(1
−
P
(0))
η,
(18)
which is used to obtain the final classical fidelity
F
class
=
N
min
+1
N
min
+2
p
+
∑
N
ph
≥
N
min+1
N
ph
+1
N
ph
+2
P
(
N
ph
)
η
(1
−
P
(0))
(19)
Supplementary References
[1] Diniz, I.
et al.
Strongly coupling a cavity to inhomogeneous ensembles of emitters: Potential
for long-lived solid-state quantum memories.
Phys. Rev. A
84,
063810 (2011).
[2] Laplane, C., Cruzeiro, E. Z., Fr ̈owis, F., Goldner, P., & Afzelius, M. High precision measurement
of the Dzyaloshinsky-Moriya interaction between two rare-earth ions in a solid.
Phys. Rev. Lett.
117,
037203 (2016). (2016).
[3] Takahashi, Y., Hagino, H., Tanaka, Y., Song, B.-S., Asano, T., & Noda, S. High-Q nanocavity
with a 2-ns photon lifetime.
Opt. Express
15,
17206-17213 (2007).
[4] James, D. F. V., Kwiat, P. G., Munro, W. J., & White A. G. Measurement of qubits.
Phys.
Rev. A
64,
052312 (2001).
[5] Massar, S., & Popescu, S. Optimal Extraction of Information from Finite Quantum Ensembles.
Phys. Rev. Lett.
74,
1259 (1995).
[6] Specht, H. P., N ̈olleke, C., Reiserer, A., Uphoff, M., Figueroa, E., Ritter, S., & Rempe, G. A
single-atom quantum memory.
Nature
473,
190-193 (2011).
[7] G ̈undogan, M., Ledingham, P. M., Almasi, A., Cristiani, M., & de Riedmatten, H. Quantum
storage of a photonic polarization qubit in a solid.
Phys. Rev. Lett.
108,
190504 (2012).
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