1. 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
Outline
Dressed systems
The dressed flux qubit
Experimental realization
Conclusion

2. Dressed systems In quantum optics
Single atom lasing of a dressed flux qubit
06/21/2012
Dressed systems In quantum optics
Atom + photon field
Energy states split
Allowed transitions (dipole moment matrix element)
Fluorescence triplet
C. Coen-Tannoudji, J. Dupont-Rock, and G. Grynberg, Atom-Photon Interactions. Basic Principles and Applications (JohnWiley, New York, 1998)

3. Dressed systems In quantum optics
Single atom lasing of a dressed flux qubit
Single atom lasing of a dressed flux qubit
06/21/2012
Dressed systems In quantum optics
Population depends on detuning
Add probe signal with different frequencies
Amplification or damping
Dressed state laser
C. 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 , (1977)

4. Theoretical discussion of the dressed flux qubit
Single atom lasing of a dressed flux qubit
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Theoretical discussion of the dressed flux qubit
Analysis of the dressed qubit is done extensively
Two interesting examples from our colleagues from Karlsruhe:
J. Hauss, A. Fedorov, C. Hutter, A. Shnirman, and Gerd Schön, Phys. Rev. Lett 100, (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 resonator
Change of the photon number statistics shows that lasing is possible
M. Marthaler, Y. Utsumi, D. S. Golubev, A. Shnirman, and Gerd Schön, Phys. Rev. Lett 107, (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)

5. The dressed flux qubit Properties of the flux qubit
Single atom lasing of a dressed flux qubit
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The dressed flux qubit Properties of the flux qubit
Tuneable two level system
Tunnel splitting D

6. The dressed flux qubit Qubit coupled to resonator
Single atom lasing of a dressed flux qubit
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The dressed flux qubit Qubit coupled to resonator
|e0>
Energies of the system (GHz)
|g1>
Exchange of energy -> change in the energy spectrum
|g0>
Energy bias (GHz)
G. Oelsner, et. al. Phys. Rev. B81, (2010)

7. The dressed flux qubit |eN-1> |gN> Splitting proportional to
Single atom lasing of a dressed flux qubit
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The dressed flux qubit
Frequency detuning (GHz)
Normalized energy (GHz)
|eN-1>
Splitting proportional to
Transform to eigenbasis
For N>>1 : g0 g1 g2 e1 e0
|gN>
Energies of the system (GHz)
Energy bias (GHz)

8. The dressed flux qubit N+1 |2> |1> G N G G N-1
Single atom lasing of a dressed flux qubit
06/21/2012
The dressed flux qubit
N+1
Assumed N=10^5 and g = 1 MHz
therefore: Tracing over N
Results in a quasi steady state
Levels |1> and |2>
|2>
|1>
With detuning role of relaxation is changed
Effective level inversion G N G G
N-1

9. The dressed flux qubit: relaxation
Single atom lasing of a dressed flux qubit
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The dressed flux qubit: relaxation
|2>
|1> d

10. Experimental realization The Sample
Single atom lasing of a dressed flux qubit
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Experimental realization The Sample
CPW (coplanar waveguide) – resonator
k= 65 kHz
Flux qubit coupled inductively
Small Ip = 12 nA
Minimize influence of flux noise
No charge noise effects observed
D = 3.6 GHz
Additional gold environment
Increase relaxation of the qubit

11. Experimental realization Implementation
Single atom lasing of a dressed flux qubit
06/21/2012
Experimental realization Implementation
System resonator – dressed qubit
Fundamental mode (2.5 GHz)
Strong Microwave field applied in harmonic of the system
Good coupling to the qubit (3H)
High photon numbers possible
|10>
|21>
Energy of system (GHz)
Possible amplification – Level inversion
Possible damping – no Level inversion
|20>
Energy bias (GHz)

12. Experimental realization Observed transmission
Single atom lasing of a dressed flux qubit
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Experimental realization Observed transmission
weakly probed around 2.5 GHz

13. Experimental realization Calculated transmission
Single atom lasing of a dressed flux qubit
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Experimental realization Calculated transmission
Fitting Parameters G/2p = 60 MHz and Gf/2p = 20MHz

14. Dependence on photon number N and detuning d
Single atom lasing of a dressed flux qubit
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Dependence on photon number N and detuning d

15. Emission from the system
Single atom lasing of a dressed flux qubit
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Emission from the system
Driving off (black):
Only thermal response
Height gives effective temperature of resonator (30 mK)
Background defined by cold amplifier
(noise about 7K)
With strong driving:
Increase of emission
Lower bandwidth
Triplet structure

16. Lasing proof Fit curve with 3 Lorentzian peaks:
Single atom lasing of a dressed flux qubit
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Lasing proof
Fit curve with 3 Lorentzian peaks:
Widths: 46 : 30 : 56 kHz
Corresponds to about
¾ : ½ : ¾ k as expected for a Mollow triplet
Reconstructed 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
[1] E.del~Valle, F.P.Laussy, Phys. Rev. A 84, (2011)

17. Single atom lasing of a dressed flux qubit
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Conclusion
The level inversion in a driven flux qubit is used to achieve lasing at the Rabi frequency
The qubit is designed for stable resonance condition and fast relaxation
The 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 basis

18. Lasers Laser prinicple
Single atom lasing of a dressed flux qubit
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Lasers Laser prinicple 3
G32
G21<< G32 nD
Stimulated emission 2
Geff 1

19. Lasers Laser prinicple
Single atom lasing of a dressed flux qubit
02/23/2012
Lasers Laser prinicple
Stimulated emission (usual many atoms)
+ cavity
= Laser
Strong coupling for single atom laser 2
Geff 1
J. McKeever, A. Boca, A.D. Boozer, J.R. Buck, and H. J. Kimble, Nature 425, 268 (2003)

20. Lasers Experimental Realization of a single atom laser
Single atom lasing of a dressed flux qubit
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Lasers Experimental Realization of a single atom laser
Strong coupling easily achieved for artificial atoms
k /2p = 1.3 MHz
Geff /2p= 320 MHz
geff /2p = 44 MHz
No laser threshold
O. Astafiev, K. Inomata, A. O. Niskanen, T. Yamamoto,
Yu. A. Pashkin, Y. Nakamura, J. S. Tsai, Nature 449, (2007)

21. Change of Spectrum with driving
Single atom lasing of a dressed flux qubit
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First vacuum Rabi splitting
Increasing photon number yields more transitions (low stairs of the Jaynes Cummings ladder)
For high power the Mollow triplet is observable in the spectrum.
Change of Spectrum with driving