Single atom lasing of a dressed flux qubit

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

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 (John. Wiley, New York, 1998 )

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 C. Coen-Tannoudji, J. Dupont-Rock, and G. Grynberg, Atom. Photon Interactions. Basic Principles and Applications (John. Wiley, New York, 1998 ) • Dressed state laser 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 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)

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

Single atom lasing of a dressed flux qubit 06/21/2012 Energies of the system (GHz) The dressed flux qubit Qubit coupled to resonator |e 0> |g 1> |g 0> Energy bias (GHz) Exchange of energy -> change in the energy spectrum G. Oelsner, et. al. Phys. Rev. B 81, 172505 (2010)

Single atom lasing of a dressed flux qubit 06/21/2012 |e. N-1> |g. N> • Splitting proportional to • Transform to eigenbasis (GHz) Normalized energy (GHz) Energies of the system The dressed flux qubit Energy bias (GHz) • For N>>1 : Frequency detuning (GHz) e 1 g 2 e 0 g 1

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

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

Single atom lasing of a dressed flux qubit 06/21/2012 Experimental realization The Sample • CPW (coplanar waveguide) – resonator Ø k= 65 k. Hz • Flux qubit coupled inductively • Small Ip = 12 n. A Ø Minimize influence of flux noise Ø No charge noise effects observed D = 3. 6 GHz • Additional gold environment Ø Increase relaxation of the qubit

Single atom lasing of a dressed flux qubit 06/21/2012 Experimental realization Implementation Energy of system (GHz) • System resonator – dressed qubit • Fundamental mode (2. 5 GHz) |10> |21> |20> Energy bias (GHz) Possible amplification – Level inversion Possible damping – no Level inversion • Strong Microwave field applied in harmonic of the system Ø Good coupling to the qubit (3 H) Ø High photon numbers possible

Single atom lasing of a dressed flux qubit 06/21/2012 Experimental realization Observed transmission • weakly probed around 2. 5 GHz

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

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

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 m. K) – Background defined by cold amplifier (noise about 7 K) • With strong driving: – Increase of emission – Lower bandwidth – Triplet structure

Single atom lasing of a dressed flux qubit 06/21/2012 Lasing proof • Fit curve with 3 Lorentzian peaks: – Widths: 46 : 30 : 56 k. Hz – Corresponds to about ¾ : ½ : ¾ k as expected for a Mollow triplet [1] E. del~Valle, F. P. Laussy, Phys. Rev. A 84, 043816 (2011) • Reconstructed coupling from previous data about 500 k. Hz • Asymmetric shape follows from incoherent drive [1] Ø 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 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

Single atom lasing of a dressed flux qubit 02/23/2012 Lasers Laser prinicple 3 G 21<< G 32 n. D 2 Geff 1 Stimulated emission

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

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 /2 p = 1. 3 MHz Geff /2 p= 320 MHz geff /2 p = 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)

Single atom lasing of a dressed flux qubit f Spectrum with driving 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.