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Single atom lasing of a dressed flux qubit

G. Oelsner, P. Macha, E. Ilichev, M. Grajcar, O. Astafiev, U. Hübner, S. Anders and H.-G. Meyer

OutlineDressed systemsThe dressed flux qubitExperimental realizationConclusionSlide2

Dressed systems In quantum opticsAtom + photon fieldEnergy states splitAllowed transitions (dipole moment matrix element)Fluorescence triplet

06/21/2012Single atom lasing of a dressed flux qubitC. Coen-Tannoudji, J. Dupont-Rock, and G. Grynberg, Atom-Photon Interactions. Basic Principles and Applications (JohnWiley, New York, 1998)Slide3

Dressed systems In quantum opticsPopulation depends on detuningAdd probe signal with different frequenciesAmplification or dampingDressed state laser

Single atom lasing of a dressed flux qubitC. Coen-Tannoudji, J. Dupont-Rock, and G. Grynberg, Atom-Photon Interactions. Basic Principles and Applications (JohnWiley, New York, 1998)

F. Y. Wu , S. Ezekiel,M. Ducloy, and B. R. Mollow,Phys. Rev. Lett. 38 1077, (1977)Single atom lasing of a dressed flux qubit

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Theoretical discussion of the dressed flux qubitAnalysis of the dressed qubit is done extensivelyTwo interesting examples from our colleagues from Karlsruhe:J. Hauss, A. Fedorov

, C. Hutter, A. Shnirman, and Gerd Schön, Phys. Rev. Lett 100, 037003 (2008)Coupling of a classical resonator to a strongly driven qubit which is described fully quantummechanically Explained are amplification and damping observed on the classical resonatorChange of the photon number statistics

shows that lasing is possibleM. Marthaler, Y. Utsumi, D. S. Golubev, A. Shnirman, and Gerd Schön, Phys. Rev. Lett 107, 093901 (2011)So called “lasing without inversion” is discussed Dissipative environment creates an enhancement of the population of the upper state of a strong driven two level system (depending again on the detuning between resonator and

qubit)

Single atom lasing of a dressed flux qubit

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The dressed flux qubitProperties of the flux qubitTuneable two level systemTunnel splitting DSingle atom lasing of a dressed flux qubit

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The dressed flux qubit

Qubit coupled to resonatorExchange of energy -> change in the energy spectrum

|g1>

|g0>

|e0>

Energy bias (GHz)

Energies of the system (GHz)

G. Oelsner, et. al. Phys. Rev. B81, 172505 (2010)

Single atom lasing of a dressed flux qubit

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The dressed flux qubit

Splitting proportional toTransform to eigenbasisFor N

>>1 :

Energy bias (GHz)

|

gN

>

|eN-1>

g0

g1

g2

e1

e0

Energies of the system (GHz)

Frequency detuning (GHz)

Normalized energy (GHz)

Single atom lasing of a dressed flux qubit

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The dressed flux qubitAssumed N=10^5 and g = 1 MHz therefore: Tracing over NResults in a quasi steady state Levels |1> and |2>

N+1

N

N-1

|2>

|1>

With detuning role of relaxation is changed

Effective level inversion

G

G

Single atom lasing of a dressed flux qubit

G

G

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The dressed flux qubit: relaxationSingle atom lasing of a dressed flux qubit

|2>

|1>

d

0

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CPW (coplanar waveguide) – resonatork= 65 kHzFlux qubit coupled inductively Small Ip = 12 nAMinimize influence of flux noise No charge noise effects observedD

= 3.6 GHzAdditional gold environmentIncrease relaxation of the qubitExperimental realizationThe Sample

Single atom lasing of a dressed flux qubit

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Experimental realization Implementation

System resonator – dressed qubitFundamental mode (2.5 GHz)Strong Microwave field applied in harmonic of the system Good coupling to the qubit (3H)High photon numbers possible

|21>

|20>

|10>

Possible amplification

– Level inversion

Possible damping

– no Level inversion

Energy bias (GHz)

Energy of system (GHz)

Single atom lasing of a dressed flux qubit

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Experimental realization Observed transmissionweakly probed around 2.5 GHz

Single atom lasing of a dressed flux qubit

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Experimental realization Calculated transmissionFitting Parameters G/2p = 60 MHz and G

f/2p = 20MHz

Single atom lasing of a dressed flux qubit06/21/2012Slide14

Dependence on photon number N and detuning d

Single atom lasing of a dressed flux qubit

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Emission from the systemDriving off (black): Only thermal responseHeight

gives effective temperature of resonator (30 mK)Background defined by cold amplifier (

noise about 7K)With strong driving: Increase of emission Lower bandwidthTriplet structureSingle atom lasing of a dressed flux qubit

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Lasing proofFit curve with 3 Lorentzian peaks:Widths: 46 : 30 : 56 kHz

Corresponds to about ¾ : ½ : ¾ k as expected for a Mollow tripletReconstructed

coupling from previous data about 500 kHz Asymmetric shape follows from incoherent drive [1]Mollow

triplet is a clear

sign

of

the

coherent

light in

the

cavity

caused

by

the

lasing

action

of

the

dressed

system

Single atom lasing of a dressed flux qubit

[1]

E.del~Valle

,

F.P.Laussy

, Phys.

Rev

. A

84

, 043816 (2011)

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ConclusionSingle atom lasing of a dressed flux qubitThe level inversion in a driven flux qubit is used to achieve lasing at the Rabi frequencyThe qubit is designed for stable resonance condition and fast relaxationThe driving field is applied in a harmonic of the resonator to achieve high photon numbers

The experimental pictures can be fitted by solving the stationary master equation in the dressed state basis06/21/2012Slide18

02/23/2012Lasers Laser prinicpleSingle atom lasing of a dressed flux qubit

3

21

n

D

G

32

G

21

<<

G

32

G

eff

Stimulated emission Slide19

02/23/2012Lasers Laser prinicpleSingle atom lasing of a dressed flux qubit

21

G

eff

Stimulated emission (usual many atoms)

+ cavity

= Laser

Strong coupling for single atom laser

J. McKeever, A. Boca, A.D. Boozer, J.R. Buck, and H. J. Kimble, Nature 425, 268 (2003)Slide20

02/23/2012Lasers Experimental Realization of a single atom laserStrong coupling easily achieved for artificial atoms k /2

p = 1.3 MHz Geff /2p= 320 MHz geff /2p = 44 MHzNo laser thresholdSingle atom lasing of a dressed flux qubit

O. Astafiev, K. Inomata, A. O. Niskanen, T. Yamamoto,Yu. A. Pashkin, Y. Nakamura, J. S. Tsai, Nature 449, 588-590 (2007)Slide21

Change of Spectrum with drivingFirst vacuum Rabi splittingIncreasing

photon number yields more transitions (low stairs of the Jaynes Cummings ladder)

For high power the Mollow triplet is observable in the spectrum.Single atom lasing of a dressed flux qubit

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