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

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)

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. 38 1077, (1977)

Theoretical discussion of the dressed flux qubit Single atom lasing of a dressed flux qubit 06/21/2012 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, 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 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, 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)

The dressed flux qubit Properties of the flux qubit Single atom lasing of a dressed flux qubit 06/21/2012 The dressed flux qubit Properties of the flux qubit Tuneable two level system Tunnel splitting D

The dressed flux qubit Qubit coupled to resonator Single atom lasing of a dressed flux qubit 06/21/2012 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, 172505 (2010)

The dressed flux qubit |eN-1> |gN> Splitting proportional to Single atom lasing of a dressed flux qubit 06/21/2012 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)

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

The dressed flux qubit: relaxation Single atom lasing of a dressed flux qubit 06/21/2012 The dressed flux qubit: relaxation |2> |1> d

Experimental realization The Sample Single atom lasing of a dressed flux qubit 06/21/2012 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

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)

Experimental realization Observed transmission Single atom lasing of a dressed flux qubit 06/21/2012 Experimental realization Observed transmission weakly probed around 2.5 GHz

Experimental realization Calculated transmission Single atom lasing of a dressed flux qubit 06/21/2012 Experimental realization Calculated transmission Fitting Parameters G/2p = 60 MHz and Gf/2p = 20MHz

Dependence on photon number N and detuning d Single atom lasing of a dressed flux qubit 06/21/2012 Dependence on photon number N and detuning d

Emission from the system Single atom lasing of a dressed flux qubit 06/21/2012 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

Lasing proof Fit curve with 3 Lorentzian peaks: Single atom lasing of a dressed flux qubit 06/21/2012 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, 043816 (2011)

Single atom lasing of a dressed flux qubit 06/21/2012 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

Lasers Laser prinicple Single atom lasing of a dressed flux qubit 02/23/2012 Lasers Laser prinicple 3 G32 G21<< G32 nD Stimulated emission 2 Geff 1

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)

Lasers Experimental Realization of a single atom laser Single atom lasing of a dressed flux qubit 02/23/2012 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, 588-590 (2007)

Change of Spectrum with driving Single atom lasing of a dressed flux qubit 06/21/2012 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