Conditional phase shift from a quantum dot in a pillar microcavity

Abstract

Large conditional phase shifts from coupled atom-cavity systems are a key
requirement for building a spin photon interface. This in turn would allow the
realisation of hybrid quantum information schemes using spin and photonic
qubits. Here we perform high resolution reflection spectroscopy of a quantum
dot resonantly coupled to a pillar microcavity. We show both the change in
reflectivity as the quantum dot is tuned through the cavity resonance, and
measure the conditional phase shift induced by the quantum dot using an ultra
stable interferometer. These techniques could be extended to the study of
charged quantum dots, where it would be possible to realise a spin photon
interface.

Full text

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arXiv:1011.0384v1 [quant-ph] 1 Nov 2010
Conditional phase shift from a quantum dot in a pillar microcavity
A.B. Young,1, ∗R. Oulton,1,2C.Y. Hu,1A.C.T. Thijssen,2C. Schneider,3S.
Reitzenstein,3M. Kamp,3S. H¨ ofling,3L. Worschech,3A. Forchel,3and J.G. Rarity1
1Merchant Venturers School of Engineering, Woodland Road Bristol, BS8 1UB
2H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, UK
3Technische Physik, Physikalisches Institut and Wilhelm Conrad R¨ ontgen-Center for Complex Material Systems,
Universit¨ at W¨ urzburg, Am Hubland, 97474 W¨ urzburg, Germany
(Dated: November 2, 2010)
Large conditional phase shifts from coupled atom-cavity systems are a key requirement for building
a spin photon interface. This in turn would allow the realisation of hybrid quantum information
schemes using spin and photonic qubits. Here we perform high resolution reflection spectroscopy of
a quantum dot resonantly coupled to a pillar microcavity. We show both the change in reflectivity
as the quantum dot is tuned through the cavity resonance, and measure the conditional phase
shift induced by the quantum dot using an ultra stable interferometer. These techniques could be
extended to the study of charged quantum dots, where it would be possible to realise a spin photon
interface.
Long term storage (and processing) of quantum super-
positions requires the development of static qubits with
long decoherence times, such as electron spins on charged
quantum dots (QD’s)1. Photons can then be used as
”flying” qubits to transfer and encode information be-
tween storage and processing nodes. An essential compo-
nent is then a high-fidelity spin-photon interface, which
can transfer information between photons and spins de-
terministically. In this paper we demonstrate the first
steps towards such a device using a quantum dot strongly
coupled to a pillar microcavity. We measure a reflec-
tion amplitude and macroscopic phase shift conditional
on an (initially uncharged) QD being in resonance with
the cavity. The conditional phase shift implies that a
singly charged dot in a similar cavity will cause large po-
larization rotations conditional on the spin state of the
electron2leading to non-demolition measurement of spin
and eventually to a spin-photon entangling device3,4, or
spin-photon interface.
The single photon has long been recognised as the
ideal transporter of quantum information encoded as
polarization5or time superpositions6. There are several
candidates for the storing of quantum information in-
cluding the ground state spins such as found in trapped
atoms7,8, ions9, colour centres in diamonds10, or electron
spins on charged QD’s1. It is the latter that is of inter-
est here because of the comparative ease of incorporat-
ing them into a solid state cavity. This would facilitate
deterministic transfer of quantum information between
photon and spins. Such an spin-photon interface is key
to building quantum repeaters11, universal gates12, and
eventually large scale quantum computers13.
The implementation of a practical conditional phase
shift measurement and spin-photon interface in a QD-
cavity system requires careful design considerations.
High quality-factor QD-cavities are now becoming rou-
tine, but if they are to be useful quantum information
devices, one must collect the photons that eventually leak
FIG. 1: a. Showing a schematic diagram of a 2.5µm dimeter
pillar with 33/26 bottom/top mirror pairs, containing a single
QD. b. SEM image of a pillar microcavity defined by electron
beam lithography and reactive ion etching.
diagram of the setup used to measure the phase shift caused
by a single QD coupled to a pillar microcavity. BS1 and BS2
are both 50:50 non-polarising beamsplitters, the soleil babinet
compensator allows us to initialise the setup with sinφ = 0.
c.
Schematic
from the cavity with a reasonably high efficiency. A high
Q-factor photonic crystal slab cavity containing a QD
has indeed been used to demonstrate a conditional phase
shift14. However, these types of cavities are designed
either for low out-of-plane losses, or for high extraction
efficiencies: it is difficult to achieve both high Q and high
extraction efficiency in the same design. Future designs
may include an efficient coupled cavity-waveguide design
to overcome this difficulty. However, a spin-photon in-
terface also requires a cavity that allows the readout of
phase as an arbitrary superposition of linear polarization
(i.e. one should be able to read out circular polarization

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without the cavity distorting the phase information). No
photonic crystal cavity design exists so far that would
meet all of these requirements. A cylindrical micropillar
cavity, however, is much more promising. The direction-
ality of the emission may be fine-tuned by choosing the
number of top distributed Bragg reflector (DBR) pairs,
such that output efficiency is increased without compro-
mising the Q-factor significantly, and its near-unity cir-
cular cross-section should lead to no birefringence in the
mode of the cavity. We demonstrate the feasibility of
such a cavity for phase shift measurements, with an eye
to an efficient spin-photon interface.
The planar microcavity structures are grown using
molecular beam epitaxy on (100) orientation GaAs sub-
strates. High reflectivity mirrors are fabricated by grow-
ing DBR’s consisting of alternating layers of GaAs and
AlAs of a quarter wave thickness, either side of a one
wavelength thick GaAs cavity with a layer of AlGaInAs
QDs formed in the cavity center. The sample used in this
experiment consists of 33/26 bottom/top mirror pairs.
Cylindrical micropillar devices are then fabricated using
high resolution electron beam lithography and reactive
ion etching16(Fig.1(b)) with an eccentricity of ǫ < 10−4.
In this experiment the micropillar has a nominal diame-
ter of 2.5µm.
The QD-cavity system can be parameterised by five
constants (Fig.1(a)), these are: κ, the decay rate for in-
tracavity photons via the top mirror (outcoupling), κs,
the decay rate for intracavity photons via the side walls
of the cylindrical micropillar, and any other losses such
as transmission and absorption, g, the QD-cavity field
coupling rate, and γ, the linewidth of the QD. We may
now express the photon reflectivity when incident on the
top of the pillar2:
r(ω) = |r(ω)|eiφ
(1)
= 1 −
κ(i(ωqd− ω) +γ
2)(i(ωc− ω) +κ
2)
(i(ωqd− ω) +γ
2+κs
2) + g2
where ωqdand ωcare the frequencies of the QD and cav-
ity, and ω is the frequency of incident photons. In this ex-
periment we aim to find the reflectivity given by |r(ω)|2,
and the associated phase shift φ.
The setup used to perform the measurements can be
seen in Fig.1(c). The waveplate is set on the input to
give diagonally polarised (+45◦) light. This then passes
through a Wollaston prism that separates the horizontal
(H) and vertical (V) component at an angle of 0.5◦. We
then use a lens with a numerical aperture (NA) of 0.5 to
focus these to two spots (∼ 3µm diameter) on our sample;
The H component is reflected from the cavity and the V
component from some unetched material on the sample.
The path difference between the two beams that form the
two arms of the interferometer is ∼100µm, resulting in
an ultra stable interferometric setup. The output signal
is then split into two by a beamsplitter (BS2). On one
arm the beam passes through a half waveplate set at
a
b
f
1333.56 1333.60
Energy (meV)
1333.64
22K
21.75K
21.5K
21.25K
21K
20.75K
20.5K

Reflectivity
20K
1333.561333.60
Energy (meV)
1333.64
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7

21.25K

(rad)
22K
21.75K
21.5K
21K
20.75K
20.5K
20K
FIG. 2: Plots showing a. the reflectivity of the QD micropil-
lar, and b.
the phase as we vary the temperature of the
sample. Since the dot energy changes quicker than the cav-
ity energy we can tune the dot through the cavity resonance,
from right to left as we increase temperature.
22.5◦which mixes the H and V components, then on to
a polarising beam splitter (PBS1) to detect diagonal (D)
and anti-diagonal (A). In the second arm we pass the
signal through a polarising beamsplitter (PBS2) so that
one channel is H and the other V. To obtain the phase we
subtract the signal in detector ”D” from that in detector
”A” to give:
D − A = r(ω)β(ω)sinφ(ω) (2)
where r(ω) is the amplitude of signal reflected from the
pillar, and β(ω) is the amplitude of the signal reflected
from the unetched region. Since the channels that mea-
sure ”H” and ”V” will give us |r(ω)|2and |β(ω)|2respec-
tively, the signal can be normalised to extract the phase.
This allows us to simultaneously measure both the in-
tensity (|r(ω)|2), and phase (φ) modulation of the QD
coupled cavity system.
To measure the amplitude and phase we perform high
resolution reflection spectroscopy, by tuning a single fre-
quency laser through the cavity resonance. The laser has
a linewidth of < 1MHz, and is attenuated to a power of
< 100pW before the objective lens. This ensures we have
< 0.1 photons per cavity lifetime (∼ 25ps). This enables
very high resolution scans of the sample to be performed
at the single photon level, where the QD transition is not
saturated. We then subsequently change the tempera-
ture of the sample to tune the QD resonance through the
cavity.
A QD-micropillar system was identified using non-
resonant photo-luminesence (PL -not shown), in which
a QD line (most likely a neutral exciton), temperature-
shifted through the cavity without crossing.
shows the change in reflectivity as a result of scanning
the laser through the same cavity and QD resonance for
different temperatures. At low temperature we have one
Fig.2(a)

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dip in intensity caused by the cavity resonance with a
Q-factor of ∼ 51000. As we increase the temperature
to 20.5K the dot approaches from the higher energy side
and can be seen to slightly modify the Lorentzian line
shape. Further increasing the temperature we bring the
dot closer to the cavity resonance, which forms a double
peak structure due to the exiton-photon hybridisation.
The dot then moves out of the other side of the cavity
at higher temperatures, without ever crossing the cavity
resonance. This anti crossing behaviour is a well known
feature associated with strong coupling17. At 22K the
dot is still just visible in the reflection spectrum.
In Fig.2(b) the corresponding measured phase shift is
plotted as the dot is temperature tuned through the cav-
ity. At low temperature there is only one phase feature
associated with the cavity resonance, but as the QD is
tuned onto resonance, a double phase feature associated
with the Rabi split dressed states is observed.
Let us now examine the data in more detail. Fig.3
shows data taken at 21K and 22K (QD on and off res-
onance) for (a) intensity and (b) phase. When the QD
and the cavity are resonantly coupled (ωqd= ωc) at 21K,
the double peak structure corresponds to the Rabi split
dressed states. From this splitting it is possible to es-
timate g ∼ 11µeV. Fitting the data using Equation 1
(Fig.3) we find that we obtain the values g = 9.4µeV,
κs = 24.7µeV, κ = 1.2µeV and γ ∼ 5µeV. This con-
firms that we are in the onset of strong coupling where
g > (κ + κs+ γ)/4.
This fit also suggests that the photon loss rate (κs) is
∼ 20 times greater than that from the top DBR. However
this ratio is determined by the depth of the features in
the reflection spectra, which is also dependant on exter-
nal mode coupling efficiency, not incorporated into Equa-
tion 1. This coupling is dependant on the external optics:
if we use a ×100 objective with a 0.7 NA (< 2µm spot
diameter) and scan the laser through the same bare cav-
ity we find that the reflection feature decreases to 45%
of the maximum value (in supporting online material),
compared to 15% for the 0.5NA objective (Fig.3(a)). As-
suming that at least a 3× larger coupling efficiency is
achievable, fitting this data implies that κs ≤ 4κ, re-
flecting previous estimates of the loss in these micropillar
structures16. By increasing the coupling efficiency we al-
ter the ratio of κs/κ, however their sum remains constant
and is the Q-factor of the cavity. As it is known that the
modematching is still not optimum with the higher NA
objective the ratio κs/κ is likely more favourable than
measured.
If we compare the results at 22K to those at 21K we ob-
serve clearly a conditional phase shift imposed on the re-
flected light from the resonantly coupled QD cavity (φd)
compared to the case of the empty cavity (φc). Fig.3(b)
contains a plot of this conditional phase shift (φd− φc).
There is a maximum phase difference of 0.05rad (2.85◦)
at 1333.596meV. The depth of the reflection feature in
Fig.3(a) has a visibility of only ∼ 0.15, implying that the
un-modematched reflected signal contributes a constant
1333.575 1333.600 1333.625
-0.06
-0.03
0.00
0.03
φ φ φ φd− φ
− φ − φ
− φc
φ φ φ φd
Energy (meV)
φ φ φ φc
-0.03
0.00
0.03
∆φ(rad)
φ(rad)
-0.06
-0.03
0.00
0.03
1333.551333.60
Energy (meV)
1333.65
0.90
0.95
1.00
Reflectivity (normalized)
rc(ω)
rd(ω)
0.90
0.95
1.00
a
b
FIG. 3: Plots showing a.
empty cavity rc = |r(ω)|2
nantly coupled QD rd = |r(ω)|2
responding phase shift for an empty cavity φc, and a cavity
with a resonantly coupled QD φd, and the conditional phase
shift φd− φc. the dashed lines represent the line of 0 phase
shift for each plot.
The relfected amplitude for an
cat 22K, and a cavity with a reso-
dat 21K. b. Shows the cor-
background of order 0.7 to the reflected signal.
ing this into account we deduce a conditional phase shift
of 0.12rad (6.7◦). Note that the phase shifts we infer
are comparable to the non-linear phase shifts measured
in previous work on photonic crystal QD-cavity systems
(12◦)15, and atom cavity systems (11◦)19. However, in
our work the phase shift is linear and conditional on the
QD being present in the cavity, not on the presence of
a control photon. Additionally the value of the phase
shift is measured directly: we do not filter the excita-
tion photons that do not interact with the cavity. This
Tak-

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means that we are able to use the probe photons directly
for use in quantum information applications. If this were
a charged dot, we would already have a giant Faraday
rotation that is three orders of magnitude larger than
has previously been measured for electron spins18. Since
measurements are performed at the single photon level it
would be possible to perform a quantum non-demolition
measurement of the spin.
Let us finally consider whether these results indicate
that these state-of-the-art QD micropillar cavities are
suitable for a spin-photon interface. One requirement
for such an interface is a conditional phase shift > π/2
between an empty cavity and a resonantly coupled QD-
cavity, this can be achieved if κ > κs. We have a deduced
phase shift of 0.12rad (6.7◦). This could be increased by
removing top mirror pairs from the DBR structure to in-
crease κ. Calculations show if g and κsremain constant
and κ is increased so that κ > κs, whilst maintaining
κ/4 ∼ g theoretically a conditional phase shift of > π/2
would be achieved. The disadvantage to working in this
regime is that the calculated reflectivity is only ∼ 20%.
This would allow us to start performing the quantum op-
erations proposed in2–4albeit with a reduced efficiency
due to intrinsic photon loss. Another requirement is an
efficient input-output coupling, for deterministic transfer
of information between photons and spins. Here we have
achieved of order 30% in our phase measurement experi-
ment, however with our ×100 objective we estimate this
to be > 70% (in supporting online material). In the fu-
ture we would expect to achieve near 100% efficiency as
has previously been shown in similar pillar structures.20
This would allow us to perform a significantly more ac-
curate measurement of the side leakage and would also
increase the observed phase shifts from the sample.
In conclusion we have shown that it is possible to mea-
sure the change in reflectivity from a micropillar caused
by coupling a single QD, using high resolution reflection
spectroscopy. We have also shown that we can deduce
a conditional phase shift of 0.12rad between an empty
cavity and a cavity with a resonantly coupled QD, using
a single photon level probe. With improved modematch-
ing and pillar design this conditional phase shift could
be much larger. The intrinsic symmetry of the micropil-
lar sample design means that the birefringence for linear
polarizations can be minimal. This paves the way for
future research using charged QDs, where, in the short
term this technique would already allow us to monitor the
spin dynamics of a single trapped electron spin strongly
coupled to a cavity, with three orders of magnitude more
accuracy than previously achieved. This area is a crucial
next-step to achieving the long-term goal of spin photon
interfaces and deterministic quantum gates.
∗Electronic address: A.Young@bristol.ac.uk
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We acknowledge support from EPSRC EP/G004366/1, EU
project 248095 Q-Essence and ERC grant 247462 QUOWSS.
This work is carried out in the Bristol Centre for NanoScience

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and Quantum Information