Page 1

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

Page 2

2

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)

Page 3

3

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-

Page 4

4

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

1T. Calarco, A. Datta, P. Fedichev, E. Pazy, and P. Zoller.

Spin-based all-optical quantum computation with quan-

tum dots: Understanding and suppressing decoherence.

Phys. Rev. A, 68(1):012310, Jul 2003.

2C. Y. Hu, A. Young, J. L. O’Brien, W. J. Munro, and

J. G. Rarity. Giant optical faraday rotation induced by

a single-electron spin in a quantum dot: Applications to

entangling remote spins via a single photon. Phys. Rev. B,

78(8):085307, Aug 2008.

3C. Y. Hu, W. J. Munro, J. L. O’Brien, and J. G. Rarity.

Proposed entanglement beam splitter using a quantum-dot

spin in a double-sided optical microcavity. Phys. Rev. B,

80(20):205326, Nov 2009.

4C. Y. Hu, W. J. Munro, and J. G. Rarity. Deterministic

photon entangler using a charged quantum dot inside a

microcavity. Phys. Rev. B, 78(12):125318, Sep 2008.

5R. Ursin, et al. Entanglement-based quantum communi-

cation over 144 km. Nature., 3:481 – 486, June 2007.

6Nicolas Gisin, Gr´ egoire Ribordy, Wolfgang Tittel, and

Hugo Zbinden. Quantum cryptography. Rev. Mod. Phys.,

74:145, 2002.

7Kimble ed P. Berman. Cavity Quantum Electrodynamics.

Academic Press Inc, Boston, 1994. p 203-266.

8C. Langer, et al. Long-lived qubit memory using atomic

ions. Physical Review Letters, 95(6):060502, 2005.

9J I Cirac and P Zoller. Quantum computation with cold

trapped ions. Phys. Rev. Lett., 74:4091–4094, 1995.

10F Jelezko, T Gaebel, I Popa, A. Gruber, and J Wrachtrup.

Observation of coherent oscillations in a single electron

spin. Phys. Rev. Lett., 92(7):076401, Feb 2004.

11Edo Waks and Jelena Vuckovic.

parency in drop-filter cavity-waveguide systems. Physical

Review Letters, 96(15):153601, 2006.

12L.-M. Duan and H. J. Kimble. Scalable photonic quantum

computation through cavity-assisted interactions.

Rev. Lett., 92(12):127902, Mar 2004.

13Ashley M. Stephens, et al. Deterministic optical quantum

computer using photonic modules. Phys. Rev. A, 78(3):

032318, Sep 2008.

14Ilya Fushman,et al. Controlled Phase Shifts with a Single

Quantum Dot. Science, 320(5877):769–772, 2008.

15Englund, et al. Controlling cavity reflectivity with a single

quantum dot. Nature, 450:857–861, 2007.

16S. Reitzenstein, et al. Alas/gaas micropillar cavities with

quality factors exceeding 150.000. Applied Physics Letters,

90(25):251109, 2007.

17Reithmaier et al. Strong coupling in a single quantum dot-

semiconductor microcavity Nature, 432:197-200, 2004

18J. Berezovsky, et al. Nondestructive Optical Measurements

of a Single Electron Spin in a Quantum Dot. Science, 314

(5807):1916–1920, 2006.

19Q A Turchette, C J Hood, W Lange, H Mabuchi, and

H J Kimble. Measurement of conditional phase shifts for

quantum logic. Phys. Rev. Lett., 75:4710–4713, 1995.

20M. T. Rakher, N. G. Stoltz, L. A. Coldren, P. M. Petroff,

and D. Bouwmeester. Externally mode-matched cavity

quantum electrodynamics with charge-tunable quantum

dots. Phys. Rev. Lett., 102(9):097403, Mar 2009.

Dipole induced trans-

Phys.

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

Page 5

5

and Quantum Information