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phys. stat. sol. (c) 5, No. 9, 2808–2815 (2008) / DOI 10.1002/pssc.200779289

© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

p s scurrent topics in solid state physics

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Probing the interaction between asingle quantum dot and a photoniccrystal cavity

Ilya Fushman1,2, Dirk Englund1,2, Andrei Faraon1,2, and Jelena Vuckovic1,*

1 Applied Physics, Stanford University, Stanford CA, 94305, USA2 These authors contributed equally

Received 12 October 2007, revised 2 January 2008, accepted 17 January 2008Published online 17 June 2008

PACS 42.50.Dv, 42.50.Pq , 42.55.Tv, 42.70.Qs

∗ Corresponding author: e-mail jela@stanford.edu

This article reviews our recent work on the developmentof nanophotonic devices for quantum information pro-cessing. We have developed a temperature tuning tech-nique, that allows us to independently tune photoniccrystal cavities and quantum dots on the same chip. Thehigh quality factor to mode volume ratio of such cavitiesleads to a strong interaction between the cavity and thequantum dot. The cavity modifies the quantum dot life-time, which, in turn, modifies the transmission propertiesof the cavity.

We observe that the resonant nonlinearity of the quantumdot is greatly enhanced by the recirculation of light, andleads to a giant optical nonlinearity, where single pho-tons are able to saturate the quantum dot and modify thetransmission function of the cavity. Along with these re-sults, we review the experimental developments, whichhave led to the realization of the experiment.

1 Introduction Our goal is the development of ar-chitecture for on-chip quantum information processing de-vices. An attractive paradigm for a quantum informationprocessing device is a network of stationary qubits that areconnected by flying photonic qubits. The stationary nodesof such a system can be atoms with two stable groundstates, or the spin states of electrons or nuclei. An opti-cal cavity can be used to efficiently transfer informationbetween the stationary qubit and the connecting photonicqubit and facilitate the interaction between the two. Thestates of the stationary qubits determine the routing of pho-tonic information in such a network. Furthermore, interac-tions between several photonic qubits, and hence remotestationary qubits, can be facilitated by the stationary qubitinside the cavity [1,2]. Towards these ends, we have beendeveloping photonic cavities, photonic networks, and theinteraction between stationary qubits and photons in theGallium Arsenide (GaAs) material system.

We have chosen GaAs due to the availability of In-dium Arsenide (InAs) quantum dots with large dipole mo-ments, and the well understood semiconductor processingtechniques for the development of high quality factor (Q),small optical mode volume (V) photonic crystal (PC) cav-ities. This system has great potential for realizing a highdensity, monolithically integrated quantum optical networkmade up of cavity nodes connected by waveguides [3]. Inthe past few years, tremendous progress has been made inthis particular subfield of quantum optics, with the devel-opment of efficient single photon sources [4], the demon-stration of strong coupling between a quantum dot and PCcavity [5,6], and the generation and transfer of single pho-tons on a PC chip [3]. The PC network architecture has theadditional benefit of being potentially useful for commer-cial photonics applications, and therefore active researchfor these applications can be transferred to the quantum in-formation processing domain. In Section 2, we review thedesign and fabrication methods for photonic crystal cavi-

© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

phys. stat. sol. (c) 5, No. 9, 2808–2815 (2008) / DOI 10.1002/pssc.200779289

ties used in our work. In Section 3 we review the theoryof coupling between quantum dots and PC cavities in thestrong and weak coupling regimes. We present our resultson the development of single photon sources and controlover the spontaneous emission rates of quantum dots in PCcavities [4]. In Section 4 we review the theory of resonantlight scattering from quantum dots coupled to PC cavities,and present our novel local temperature tuning technique[7], which allows us to resonantly probe the quantum dotinside the PC cavity. We show that the dot strongly modi-fies the cavity spectrum, and acts as a saturable nonlinear-ity at powers corresponding to a single photon per cavitylifetime [8], and discuss the implications for coherent con-trol on the photonic crystal chip.

2 Photonic crystal design and fabrication Ourexperiments are based on planar photonic crystal (PC) de-vices in GaAs with incorporated InAs quantum dots (QDs).QD wafers are grown by molecular beam epitaxy by ourcollaborators. They contain an active region consisting ofa 150-160 nm thick GaAs layer with a centered InAs/GaAsQD layer. The active layer is grown on an AlGaAs sacrifi-cial layer (with Al content of 80%), which is in turn grownon a GaAs substrate. The suspended PC structures are fab-ricated on such a wafer by a combination of electron beamlithography and dry etching (which creates a PC pattern inthe top GaAs layer containing QDs), and a final wet etch-ing step which removes a sacrificial layer underneath PCcomponents. An example of fabricated GaAs PC cavitiesusing the described procedure is shown in Fig. 1. In thesame figure we also show the photoluminescence spectrumfrom the same type of cavity, obtained by exciting embed-ded InAs QDs, and indicating a cavity quality (Q) factor of20000.

3 Interaction between coherent light and aquantum dot in a PC cavity: theory The theory ofan emitter coupled to an optical cavity can be found in [9,2]. The novelty of photonic crystal cavities is that the op-tical mode volume is very small (on the order of (λ/n)3,where n is the refractive index of the material, and λ isthe resonant wavelength of the cavity), and therefore evenwith moderate quality factors, highly nonlinear effects canoccur in this system.

We consider the quantum dot to be a two level sys-tem with a long-lived ground state, and a dipole decay rateγ/2π = 0.2 GHz. InAs quantum dots at low temperature(≈ 10 − 20 K) are generally close to Fourier-limited, andso the dipole dephasing rate can be approximated to be onehalf of the dipole decay rate. The coupling of the quantumdot dipole to the cavity electric field is given by the Rabifrequency:

g =|µ|h

√hωd

2εMV

E(r)|E(rM |cos

(µ · e|µ|

)(1)

In this expression, rM is the point where the cavity modefield E(r) has a maximum, e is the unit vector along thedirection of E(r), εM is the dielectric constant at thispoint, µ is the dot dipole moment, ωd is the dot emissionfrequency, and V is the optical mode volume defined asV =

Rd3rε(r)|E(r)|2εM |E(rM )|2 ≈ 0.75

(λn

)3. Values of g clearly de-

pend on position and dipole alignment, with the maximumdipole moment of gmax ≈ 300 GHz in this system.

When a quantum dot is resonant with the PC cavity atfrequency ωc, the dot emission is modified. The degree ofmodification depends on the parameters g, γ and the fielddecay rate κ = ωc/(2Q). In the frame rotating with the dotfrequency, the eigenvalues of the cavity-dot system are:

ω± = iωc + ωd

2−

(κ + γ

2

)±

√(κ − γ

2

)2

− g2 (2)

This equation can be taken to two limits, one in which thesquare root is real, and the other, in which it is imaginary.In the first case, the two eigenvalues are real and corre-spond to decay rates of the cavity and quantum dot. Thisregime is typically termed the weak coupling regime. In thecase of an imaginary square root, the composite quantumdot system decays at one rate, and oscillates at two fre-quencies corresponding to the coherent exchange of pho-tons between the dot and cavity.

3.1 Weak coupling regime For our system, κ/2π ≈16GHz, The eigenvalues on the weak coupling regime canbe found by expanding the square root in Eq. (2) for thecase κ >> g >> γ as:

ω+ = −(

γ +g2

κ

)≈ −g2

κ(3)

ω− ≈ −κ (4)

In this case, ω− corresponds to the cavity and ω+ cor-responds to the dot dipole. The dot excited state populationdecays with a rate 2ω+ inside the cavity. As can be seen,the value of the dot decay is modified relative to the bulkvalue γ. The ratio of the lifetime in the cavity γc to that inthe bulk γc/γ = 2ω+/γ is dependent on position, dipolealignment and frequency detuning according to

γc

γ=

34π2

Q

V

(λ

n

)3

(5)

×(

E(r)E(rM )

)2 (µ · e|µ|

)2 1

1 + 4Q2(

ωc

ωd− 1

)2

(6)

At the point of maximum spatial and frequency align-ment, the ratio γc/γ reduces to the Purcell factor F =

34π2

QV

(λn

)3. The fraction of photons emitted into the single

cavity mode is then β = Ff+F , where f accounts for the re-

duction in the available states inside the photonic bandgapmaterial.

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phys. stat. sol. (c) 5, No. 9 (2008) 2809

(a)

944 944.2 944.4 944.6 944.8 9450

200

400

600

800

1000

1200

λ (nm)

a.u

.

spectrumFit

Q=20,000

(b) Figure 1 A scanning electron micrograph(SEM) of a fabricated L3 cavity is shown in(a). The inset shows the electric field ampli-tude, computed with Finite Difference TimeDomain software, overlaid on the SEM im-age. (b) Shows a typical cavity spectrum il-luminated by InAs quantum dots that arecoupled to the cavity. A Q of 20,000 is in-ferred from the fit.

We now review our experiment, in which we haveshown that the emission rate of dots can be both suppressedand enhanced by the interaction with the cavity [4]. Spatialand spectral alignment can result in up to ten-fold enhance-ment or almost ten-fold suppression of the dot radiativerate when compared to the bulk rate (Figs. 2 and 3), with a100-fold enhancement being theoretically possible for thevalues of Q and V used in this experiment. In Fig. 2(a), thelifetimes of cavity coupled and quantum dots are derivedfrom the time-dependent photoluminescence signal. Sup-pression and enhancement relative to the bulk lifetime of≈ 1ns are observed. To show that the photonic bandgapalso suppresses the emission rate, we show the rate for aquantum dot which is inside the cavity, but emitting at 90o

relative to the cavity polarization. One of the most impor-tant applications to quantum optics is the generation of fast,efficiently extracted and indistinguishable single photons.important applications for indistinguishable single photonsources. Figure 2 (b) and (c) show the autocorrelation func-tion for quantum dots inside the PC cavity, which are bothenhanced (b) and suppressed (c). Both show strong anti-bunching at zero time delay, indicating that these are goodsingle photon sources. The larger width of peaks in (b)indicates that this dot is slowly emitting, as confirmed in(a). Our results indicate that spectral and spatial alignmenthave a great impact on dot radiative properties, and thatspectral alignment can be used to control absorption andemission rates of InAs quantum dots in PC cavities. Whilespatial alignment is in our case probabilistic, other groupshave made significant progress towards precise alignmentsof the dot position and dipole moment to the PC cavity [6].

3.2 Strong coupling regime In the strong cou-pling regime, as in the weak coupling regime, the eigen-values of the cavity and dot can be found from Eq. (2)with the condition that g ≥ κ

2 . In this case the square rootbecomes imaginary. The cavity and quantum dot cannot betreated separately, but exist in a time dependent superpo-sition state, with photons exchanging energy between the

two at a rate of ≈ 2g. The eigenvalues of this system are

ω± = − (κ + γ)2

± i

√g2 −

(κ − γ

2

)2

(7)

≈ − (κ + γ)2

± ig (8)

By improving the fabrication of our PC cavities, we havebeen able to fabricate cavities with Q’s in the range of10000 to 15000, with the best case of 25,500. In such cav-ities, we have been able to observe strong coupling. Figure4 shows a scanning electron microscope (SEM) image ofsuch a cavity with Q=10,500 and the photoluminescenceobserved from the cavity as a quantum dot is tuned throughthe cavity resonance via temperature. However, since thedot is strongly coupled to the cavity, the dot line nevercrosses the cavity line. Instead, when the two are exactlyon resonance, we observe the characteristic splitting pre-dicted by Eq. (8). For clarity, we track the quantum dot andcavity peaks at the different temperature points and plotthem in Fig. 4 (c).

The polariton splitting is on the order of 0.05nm, whichis equal to the field decay rate κ, suggesting that we operateat the onset of strong coupling with 2g/2π = 16GHz =κ/2π, where a full Rabi oscillation does not occur.

4 Interaction between coherent light and aquantum dot in a PC cavity: experiment The stronginteraction between a quantum dot and a cavity in a PCarchitecture can be used to create logic gates and nodesin a quantum network, based on several quantum informa-tion processing schemes [1,2]. These proposals rely on themodification of the cavity transmission due to the presenceof a coupled atom or quantum dot. When the quantum dotis coupled to the PC cavity, it can prohibit photons frompassing through it. Furthermore, the quantum dot behavesas a saturable absorber at very low powers [10], and, be-cause most photons are radiated into a single mode in PCcavities, it can be used as a Kerr medium for the realizationof quantum gates.

4.1 Theory The theory for the transmission functionof a cavity containing a well coupled emitter under weakexcitation can be found in [9,2], and has been extendedto the strong excitation regime in [11,10]. The analytical

2810 I. Fushman et al.: Interaction between a single quantum dot and a photonic crystal cavity

© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-c.com

ph

ysic

ap s sstat

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solid

i c

0 600 1200

A

B C

t(ps)

Inte

nsity

(no

rmal

ized

) =650ps

=3.8 ns

0

(a)

A90o

=2.9 ns

(b)

0 10452

(c)

t'(ns)

dot A

dot B

coun

ts0

0

coun

ts

=4.2 nsC

Figure 2 (a) Lifetime measurementson different QDs positioned at variouspoints inside a PC cavity. The normalizedintensity for three quantum dots A,B andC coupled to a PC cavity mode is shownas a function of time. The signal fromquantum dot A along the polarization or-thogonal to the PC cavity is shown alongA90◦. The emission rates of cavity cou-pled dots (A) are enhanced, while emis-sion of uncoupled (B,C) and dots orthog-onal to the cavity mode (A90◦) is sup-pressed. (b,c) Measurements of the pho-ton autocorrelation function on quantumdots A and B in (a). In both cases, anti-bunching at τ = 0 indicates that singleemitters are probed. The emission rate ofquantum dot A is enhanced by the cavity,while that of quantum dot B (c) is sup-pressed, as can be seed from the width ofthe autocorrelation peaks in (a,b).

Figure 3 Spontaneous emission ratemodification. (a) Experimental (circles)and calculated (bars) data of γc/γ of sin-gle QD lines vs. spectral detuning (nor-malized by the cavity linewidth λc/Q).Coupling was verified by spectral align-ment and polarization matching. (b) Il-lustration of the predicted spontaneousemission rate modification in the PC asfunction of normalized spatial and spec-tral misalignment from the cavity (a isthe lattice periodicity). This plot assumesQ = 1000 and polarization matching be-tween the emitter dipole and cavity field.The actual spontaneous emission ratemodification varies significantly with ex-act QD location.

form of the transmission is given by

R = η

∣∣∣∣∣ κ

i(ωc − ω) + κ + g2

i(ωd−ω)+γ

∣∣∣∣∣2

(9)

A plot of this function is shown in Fig. 5. It can be seenthat the quantum dot strongly modifies the transmissionproperty of the PC cavity. In particular, photons fallingwithin the bandwidth given by the QD’s modified spon-taneous emission rate g2

κ are rejected from the cavity. Thiseffect can be observed in both the weak and strong cou-pling regimes, with the bandwidth of the modified spec-trum increasing with higher coupling and higher Q. In or-der to probe this effect, we used a narrow-bandwidth (5MHz) tunable external cavity diode laser (Sacher Laser).However, scanning the laser through the cavity line andnormalizing by the input power proved difficult, since the

bandwidth of the cavity is quite large when compared tothe modehop-free tuning range of the laser.

4.2 Temperature tuning To obtain the best signalto noise in our measurement, we choose to fix the probelaser frequency, and modulate the cavity and dot resonanceusing our temperature tuning technique, developed in [7].While this proves to be a useful tool for our experiment,the most important impact of this tuning technique is thatit allows us to independently tune multiple PC nodes con-sisting of dots in cavities into resonance with each other.This bypasses the problem of dot and cavity alignmentcaused by fabrication imperfections and the large inhomo-geneous QD broadening, which have been considered to bethe biggest impediment to scaling up to quantum networksbased on multiple cavities and dots interacting with eachother. Our in-situ technique allows extremely precise spec-tral tuning of InAs quantum dots by up to 1.8nm and ofcavities of up to 0.4 nm (4 cavity linewidths). The tech-

InvitedInvited

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phys. stat. sol. (c) 5, No. 9 (2008) 2811

-2

000.11.010100

-50

5

x/a

decoupled QDscoupled QD

0.2 floor0.1 1.0 10

(b)pled

decoupled

|100

o1.0

0.1

10.0

o

(a)

cav cav

934.5 935 935.5 936

T=33.00K

T=33.40K

T=33.80K

T=34.20K

T=34.60K

T=34.65K

T=34.70K

T=34.80K

T=35.20K

T=35.60K

T=36.00K

T=36.40K

T=36.80K

(nm)33 34 35 36 37

935.1

935.15

935.2

935.25

935.3

935.35

935.4

Anti-Crossing

T[K]

[nm

]

(a)

200 nm

(b)

(c)

Figure 4 (a) Scanning electron micro-scope (SEM) image of a PC cavity inwhich strong coupling is observed. (b)Photoluminescence of a quantum dotstrongly coupled to a photonic crys-tal cavity, for different detunings be-tween the cavity and dot. The dot wave-length is controlled by the temperatureof the sample, which is controlled bythe cryostat. The cold-cavity Q-factor isaround 10500, and the mode volume is≈ 0.75 (λ/n)3 . (c) Peak positions ofphotoluminescence in Panel (b) as a func-tion of temperature. The dot and cavityline never cross, indicating that they be-have as predicted for the strong couplingregime.

( c )/

R

g=g=g=

Figure 5 Transmission of a cavity containing a coupled quantumdot on resonance with the cavity mode for several values of the cou-pling parameter g, as predicted by Eq. ( 9). When the dot is decou-pled from the cavity g = 0, the transmission function is a Lorentzianwith a linewidth corresponding to the cavity Q. When the dot is cou-pled, photons cannot pass at the cavity resonance. The bandwidth ofthe rejection window increases with larger coupling.

nique is crucial for spectrally aligning distinct quantumdots on a photonic crystal chip and forms an essential steptoward creating on-chip quantum information processingdevices.

To achieve independent on-chip tuning, distinct re-gions of the chip must be kept at different temperatures.We achieve this by thermally insulating individual cavitiesfrom the rest of the sample via trenches, thus overcomingthe good thermal conductivity of bulk GaAs. The fab-ricated tuning structure is shown in Fig. 6. The tuningbehavior of the quantum dot and the cavity is shown inFig. 7. The quantum dot resonance depends quadraticallyon power, consistent with the bandgap change, while thecavity is sensitive to the refractive index change and tunes

at 1/3 to 1/4 the rate of the quantum dot. We further verifythat the heating does not perturb the single quantum dotin the PC cavity, and that it still acts as a single photonsource, indicating that this technique is compatible with aquantum device. Thus, rather than altering the temperatureof the cryostat, we use local heating to tune a quantum dotinto strong coupling, similarly to Fig. 4.

4.3 Cavity reflectivity Using the device structureshown in Fig. 6, we measured the reflectivity of a PC cav-ity with a highly coupled dot. We start with a quantum dot,which exhibits an anticrossing with the cavity mode, asshown in Fig. 8 (a). During the experiment, the probinglaser frequency is fixed to lie closely to the point where thetemperature tuned quantum dot intersects the cavity reso-

2812 I. Fushman et al.: Interaction between a single quantum dot and a photonic crystal cavity

© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-c.com

ph

ysic

ap s sstat

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solid

i c

Figure 6 Scanning electron microscope image of the fabricated structure show-ing the PC cavity, the heating pad and the connection bridges. The temperatureof the structure is controlled with a laser diode (960 nm) focused on the heatingpad. We use 960 nm in order to prevent excitation of the quantum dots by carriergeneration or resonant pumping.

914.5 915 915.50

2

4

6

8

10

12

[nm]

0.00

0.60

1.20

1.80

2.40

3.00

3.60

4.20

4.80

Heating (960 nm)Laser Power [mW] w = 320 nm

Tchip

= 10 K

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

P [mW]

[nm

]

w = 320 nmTchip = 10 K

906 907 908 909100

150

200

250

300

[nm]

960nm Laser Power

w = 320 nm

Tchip

= 10 K

0.0 mW0.6 mW1.2 mW1.8 mW2.4 mW3.0 mW

0 500 1000 15000

0.5

1

1.5

T2 [K2]

[nm

]

(a) b

-20 -10 0 10 200

0.2

0.4

0.6

0.8

1

Time [ns]

Cou

nts

(b)

(c) (d)

Figure 7 (a) Quantum dot tuning vs. heating pump power. Thestructure is connected to the substrate by bridges measuring 320 nmin width. The quantum dot emission shifts by 1.4 nm while increas-ing the heating laser power to 3 mW. Only a small fraction of theheating laser power is absorbed in the metal pad. (b) Autocorrelationmeasurement showing single photon anti bunching while the QD wasdetuned by 0.8 nm using the local tuning technique. (c) Detuning ofthe PC cavity resonance with increasing temperature due to localheating. (d) Dependence of the PC cavity resonance wavelength onthe local heating power. The inset shows that the dot wavelength islinear with T 2. The connecting bridges had a width of 320 nm andthe cryostat was set to a base temperature of 10 K.

nance. Our temperature tuning technique is then used totune both, the dot and the cavity through the laser line.Since the dot tunes faster than the cavity, we are able totune the dot through the anticrossing point, and monitorthis with the probe beam. In order to reject the direct laserscatter, we send in a vertically polarized probe beam at 45degrees to the cavity. The light which is coupled to the cav-ity is reemitted with a horizontal component. We observethis horizontal component after a polarizing beam cube.Thus we are able to reject a large fraction of the directlyscattered light.

The results of the measurement are shown in Fig. 8(b).From the width of the splitting in (a), we obtain a valueof g/2π = 8 GHz= κ/2. As expected from the theoryin Eq. (9), the cavity reflectivity is strongly modified. Theobserved reflectivity does not drop down directly to zeroat the dot resonance. We attribute this discrepancy to ex-perimental noise. In particular, we observed that the tem-perature of the heating laser fluctuated by 0.7%, whichresulted in a fluctuation of the quantum dot on the orderof 0.005 nm. We obtain good agreement with the theory,when account for this fluctuation. The coupling efficiencywas found to be 2%.

Finally, we explore the nonlinear behavior of this sys-tem, by increasing the power of the probing laser. Asshown in Fig. 8(c), we observe saturation at power levelswhich correspond to several photons in the cavity, whichindicates one of the largest optical nonlinearities availablein the solid state systems. The major advantage of thisnonlinearity is that photons are conserved, because theyare primarily re-emitted into the cavity mode. While ourcurrent coupling efficiency of 2% is quite low, this can begreatly improved when the probe laser is coupled to thecavity via a waveguide, and this nonlinearity can be usedfor on-chip photon-photon interactions.

5 Conclusion In conclusion, we have presented ourrecent progress toward the realization of a quantum infor-mation processing network on a chip. We have been able tocreate devices that allow us to explore the weak and strongcoupling regimes for InAs quantum dots in PC cavities.We have developed a novel technique for independent fre-quency tuning of quantum dots and cavities on the samechip, and have applied this technique to a spectroscopicmeasurement of a single quantum dot in a PC cavity. Thismeasurement has revealed that the presence of the quan-tum dot can strongly alter the transmission function for the

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phys. stat. sol. (c) 5, No. 9 (2008) 2813

0 20 40 60

25 nW

100 nW

300 nW

1 W

3 W

8 W

temperature scan count

0

R (experiment)R (theory)R (empty cavity)

=0.015

0.060

0.18

0.60

1.8

4.8

0

0

0

0

0

0

inc. power=

inc. power=ncav

n =cav

n =cav

n =cav

n =cav

refle

cted

inte

nsity

(no

rmal

ized

)

n =cav

50 100 150 200

0.2

0.4

0.6

0.8

1

scan count

Inte

nsity

(no

rmal

ized

)

50 100 150 200 250

926.6

926.8

927.0

927.2

(nm

)

R (theory)R (Eq. 2)R (experiment)

QDCavity

probe A

=0.021nm(0.83g)

probe A

(a)

926.5 926.7 926.9

CavityCavityyy

(c)(b)temperature scan count

spec

tra

(tem

pera

ture

)

wavelength (nm)

Figure 8 (a) A strongly coupled quantum dot, which exhibits anticrossing with a coupling g/2π = 8 GHz= κ/2 is resonantly probed.Spectra at different values of temperature show how the dot traverses the cavity. (b) The probing laser (probe A) frequency is set closelyto the point of anticrossing as shown in the bottom panel. The temperature tuning shifts both, the dot (QD) and cavity (Cavity) linesthrough the probe. The temperature tuning is driven by a triangular wave. In the top panel of (b) we show the amplitude of the reflectedbeam, which traces out the cavity reflectivity. A fit to the theory (Eq. (9)) with cavity and dot parameters taken from spectral data in (a)matches the experimental data. When we take thermal fluctuations due to heating laser power stability into account in our theory, thefit matches the data very well. In (c) we progressively increase the power of the probe laser. We observe that the dip begins to saturateat powers, which correspond to ≈ 1 photon inside the cavity per cavity lifetime. The powers were measured before the objective lens,while photon numbers are obtained from theoretical fits.

PC cavity, and could serve as a state readout method for acoupled quantum dot. This same effect can be exploited toroute quantum information carrying photons on a chip andrealize entanglement between nodes in a quantum network.The giant optical nonlinearity will be further explored asa means to realize conditional phase gates and switching.A Kerr nonlinearity such as the one shown in our exper-iment is attractive for a photon-photon switching device.The architecture of the PC circuit, and the fact that photonsare conserved inside the propagation channel due to a highvalue of β, makes this an ideal system for multiply cas-caded nonlinear gates operating on single photons. A sim-ilar concept has been realized in atomic physics [12], butdue to the macroscopic nature of the experiment, scalingand cascading is difficult. Furthermore, this value of non-linearity can be used to realize switching at fundamentallylowest power levels given by energies of single photonsmediated by a single atom, and may find applications inmoderately powered classical information processing de-vices.

Acknowledgements We thank Nick Stoltz in the PierrePetroff group at University of California at Santa Barbara for pro-viding us with quantum dot samples used in the work on strong

coupling. We thank Bingyang Zhang in the Yoshihisa YamamotoGroup at Stanford University for providing us with samples forwork on single photon sources. Financial support was providedby the ONR Young Investigator Award and MURI Center for pho-tonic quantum information systems (ARO/DTO Program). D.E.and I.F. were also supported by the NDSEG fellowship. Workwas performed in part at the Stanford Nanofabrication Facility ofNNIN supported by the National Science Foundation.

2814 I. Fushman et al.: Interaction between a single quantum dot and a photonic crystal cavity

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