Sisyphus cooling and pumping of linear oscillator by superconducting qubit M. Grajcar Comenius University, Slovakia A. Izmalkov, S.H.W. van der Ploeg, Th. Wagner, E. I’lichev, H.-G. Meyer Institute for Physical High Technology, Germany A. Fedorov, A. Shnirman, Gerd Schön, Institut für Theoretische Festkörperphysik Universität Karlsruhe, Germany S.N. Shevchenko, A.N. Omelyanchouk, B.Verkin Institute for Low Temperature Physics and Engineering, Kharkov, Ukraine S. Ashhab, J.R. Johansson, A. Zagoskin and Franco Nori, The Institute of Physical and Chemical Research (RIKEN), Wako-shi, Japan

Outline Superconducting flux qubit Adiabatic measurement of the qubit in the ground state Spectroscopic measurement Sisyphus cooling and pumping Lower limit on the achievable temperature

Single-junction interferometer (RF-SQUID) 1 Or in normalized Units: Classical two level System!

Classical picture 1  p 2p f Particle with mass ~ CJ in potential:

Quantum Picture d p 2p f If CJ is small enough tunneling between both wells becomes possible and therefore the degeneracy is lifted. So we need Small Josephson Junctions with EJ/EC~10-100

Persistent current (flux) qubit – analogue of ammonia molecule nF B Superconducting persistent current qubit – oscillation of a magnetic dipole moment (magnetic flux), Ammonia molecule – oscillation of an electric dipole moment (f=24 GHz) N H + + H + H

Size problem and solution For quantum behavior EJ/EC~10-100 Typical parameters for aluminum technology :

Solution of the size problem ‚Size‘ problem solved in 70´s T. Yamashita et al., J. Appl. Phys. 50, 3547 (1979) This idea was dusted off by J.E. Mooij et al., Science 285, 1036, 1999

Hamiltonian. Energy surface.

Tunneling amplitude   GHz -0 0 E0 ЕС=5 GHz, g=EJ/EC=66, ЕJ=330 GHz.  0.85 0.86 0.87 0.88 0.89 0.9 0.901 0.902 0.905 0.91 0.92  GHz 20 13 8.45 5.44 3.49 2.24 2.14 2.05 1.79 1.43

Pseudospin Hamiltonian IC, f2 IC, f1 aIC (0.5<a<1) Fx 1 um

Flux qubit coupled to oscillator VT LT L CT Ib M

Adiabatic measurement away from degeneracy point

Adiabatic measurement at degeneracy point

Lagrangian of the qubit-resonator system Expanding into Taylor series up to the second order term 2

Φi Quantum approach C L L I is satisfied. At the degeneracy point b No perturbation of the measured observable [V.B. Braginsky and F.Ya. Khalili, Quantum Measurement, (Cambridge University Press, Cambridge, 1992]. The sufficient condiction for Quantum Nondemolition Measurements is satisfied.

Impedance Measurement, classical resonator LT L CT Φ VT Ib Build a resonator, connect something to it with a susceptibility different from zero and it will change its resonant frequency. Ya. S. Greenberg et al., PRB 66, 214525 (2002) DC-Squid Josephson Inductance: A. Lupascu et al., PRL 93, 177006 (2004).

Response of resonator   GHz EJ/Ec<102 =0.9 EJ/Ec103 =0.8  0.86 0.88 0.9 0.901 0.902 0.905 0.91 0.92  GHz 13 5.44 2.24 2.14 2.05 1.79 1.43

Resonant frequency of the resonator Y. Greenberg et al., PRB 66 214525 (2002). Fitting parameters

Sisyphus work Greek mythology As a punishment from the gods for his trickery, Sisyphus was compelled to roll a huge rock up a steep hill, but before he reached the top of the hill, the rock always escaped him and he had to begin again. Titian (1549) artist vision of Sisyphus work Physical realization: For atoms D. J. Wineland, J. Dalibard and C. Cohen-Tannouji, J. Opt. Soc. B9, 3242 (1992). For qubit Grajcar et al., arXiv:0708.0665 Nature Physics 4, 612-616 (2008).

Sisyphus cooling

Sisyphus pumping

Adiabatic vs. spectroscopic measurement Solid line is theoretical curve for Parameters determined from adiabatic measurement

Strong microwave driving at fmw=4.5 GHz Strong driving Transition from weak to strong driving Weak driving dc (0) A. Izmalkov et al., PRL 101, 017003 (2008) W.D. Oliver et al.,SCIENCE 310, 1653(2005) M. Sillanpää et al., PRL 96, 187002 (2006)

Landau-Zener interferometry A.V. Shytov, D.A. Ivanov, and M.V. Feigel’man, Eur. Phys. J. B 36, 263 (2003). S.N. Shevchenko et al. Phys. Rev. B 78, 174527 (2008)

More rigorous treatment of Sisyphus cooling/pumping A. Fedorov, A. Shnirman, Gerd Schön fmw=14 GHz M. Grajcar et al., Nature Physics 4, 612-616 (2008).

Spectral density of the voltage noise of the tank fmw=8 GHz

Tank circuit coupled to mechanical oscillator

Sisyphus and sideband cooling limit M. Grajcar, A. Ashhab, J.R. Johansson, F. Nori Phys. Rev. B 78, 035406 (2008)

Conclusions Superconducting flux qubits are well described by two-level (pseudospin) Hamiltonian Experimental data obtained from adiabatic and spectroscopic measurement are consistent and fully agree with the quantum-mechanical predictions to the experimental accuracy. The qubit can be used as an artificial atom for Sisyphus cooling of a low frequency oscillator (electrical, nanomechanical, etc.)

Ground state energy modulation  -  + - + m= -1/2 m= 1/2

Sisyphus cooling

Design for spectroscopic measurement

Spectroscopy of the system of two coupled flux qubits. A. Izmalkov et al., PRL 101, 017003 (2008) Without microwave driving fmw= 14 GHz fmw= 18 GHz fmw= 21 GHz

Nanomechanical oscillators Nanobridge from IPHT Jena Neik et al., Nature 443, 193 - 196 (2006) I. Martin, A. Shnirman, Lin Tian, P. Zoller Ground state cooling of mechanical resonators Phys. Rev. B 69, 125339 (2004) Prepared for measurement at temprature below1 mK in ulra low temp. lab in Košice

Quantum metamaterials Design of high efficiency microwave photon detector for GHz range G. Romero et al., Microwave Photon Detector in Circuit QED, arXiv:0811.3909v1

Four qubit sample q3 q1 q4 q2 Layout Micrograph A3 Iq3 Iq1 A2 Ib4 Iq2

Anti-Ferromagnetic and Ferromagnetic Coupling AFM FM Iq2=-10 µA Iq3=0 Iq4=-250 µA

Theoretical fits. Phys. Rev. Lett. 96, 047006 (2006) Experiment Theory

Psedo-spin Hamiltonian