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Single atom lasing of a dressed flux qubit G. Oelsner, P. Macha, E. Ilichev, M. Grajcar, O. Astafiev, U. Hbner, S. Anders and H.-G. Meyer Outline Dressed systems The dressed flux qubit Experimental realization Conclusion

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

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

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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 Schn, 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 Schn, 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 qubit06/21/2012

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The dressed flux qubit Properties of the flux qubit Tuneable two level system Tunnel splitting Single atom lasing of a dressed flux qubit06/21/2012

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The dressed flux qubit Qubit coupled to resonator Exchange 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 qubit06/21/2012

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The dressed flux qubit Splitting proportional to Transform to eigenbasis For N>>1 : Energy bias (GHz) |gN> |eN-1> g0 g1 g2e1 e0 Energies of the system (GHz) Frequency detuning (GHz) Normalized energy (GHz) Single atom lasing of a dressed flux qubit 06/21/2012

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The dressed flux qubit Assumed N=10^5 and g = 1 MHz therefore: Tracing over N Results 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 Single atom lasing of a dressed flux qubit 06/21/2012

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The dressed flux qubit: relaxation Single atom lasing of a dressed flux qubit |2> |1> 0 06/21/2012

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CPW (coplanar waveguide) resonator = 65 kHz Flux qubit coupled inductively Small Ip = 12 nA Minimize influence of flux noise No charge noise effects observed = 3.6 GHz Additional gold environment Increase relaxation of the qubit Experimental realization The Sample Single atom lasing of a dressed flux qubit06/21/2012

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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 |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 qubit06/21/2012

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Experimental realization Observed transmission weakly probed around 2.5 GHz Single atom lasing of a dressed flux qubit06/21/2012

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Experimental realization Calculated transmission Fitting Parameters = 60 MHz and = 20MHz Single atom lasing of a dressed flux qubit06/21/2012

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Dependence on photon number N and detuning Single atom lasing of a dressed flux qubit06/21/2012

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

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Lasing proof Fit curve with 3 Lorentzian peaks: Widths: 46 : 30 : 56 kHz Corresponds to about : : 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 Single atom lasing of a dressed flux qubit [1] E.del~Valle, F.P.Laussy, Phys. Rev. A 84, 043816 (2011) 06/21/2012

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

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02/23/2012 Lasers Laser prinicple Single atom lasing of a dressed flux qubit 3 2 1 D 21