Lasing with a disordered quantum metamaterial, Karlsruhe Institute of Technology (KIT) KIT University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz Association www.kit.edu
Topics Implementation of a quantum metamaterial, P. Macha, G. Oelsner, J.-M. Reiner, M. Marthaler, S. André, G. Schön, U. Huebner, H.-G. Meyer, E. Il'ichev, A. V. Ustinov, Nature Communications 5, 5146 (2014). Lasing without Inversion in Circuit Quantum Electrodynamics, M. Marthaler, Y. Utsumi, D. S. Golubev, A. Shnirman, G. Schön, Phys. Rev. Lett. 107, 093901 (2011) Lasing and disorder very recent work, mostly by Martin Koppenhöfer 2 6/3/15
Quantum metamaterials Pascal Macha, Gregor Oelsner, Jan-Michael Reiner,, Stephan Andre, Gerd Schön, Uwe Hubner, HansGeorg Meyer, Evgeni Il ichev and Alexey V. Ustinov, Nat. Comm. 5, 5146 (2014). 3 6/3/15
Quantum metamaterials Tavis-Cummings Model: By driving the third mode it is possible to shift the energy splittings of the qubits. 4 6/3/15
Quantum metamaterials Tavis-Cummings Model: By driving e.g. the third mode it is possible to shift the energy splittings of the qubits. 5 6/3/15
Disorder in quantum metamaterials Pascal Macha, PhD Thesis 6 6/3/15
Outline 1. Introduction 2. Qubit Lasing with Flux Qubits 3. Quantum Heat Engine and Lasing 4. Lasing with strong Disorder 5. Conclusion 7 6/3/15
Lasing Stimulated emission Stimulated absorption G. Oelsner, P. Macha, O. V. Astafiev, E. Il ichev, M. Grajcar, U. Hübner, B. I. Ivanov, P. Neilinger, and H.-G. Meyer, Phys. Rev. Lett. 110, 053602 (2013). 8 6/3/15
Lasing: Population inversion Breaking the symmetry: Population inversion is characterized by G. Oelsner, P. Macha, O. V. Astafiev, E. Il ichev, M. Grajcar, U. Hübner, B. I. Ivanov, P. Neilinger, and H.-G. Meyer, Phys. Rev. Lett. 110, 053602 (2013). 9 6/3/15 where the average is calculated without coupling to the photon field.
Qubit Lasing: Dressed State Lasing Dressed State Lasing: Frequency of the driving field: G. Oelsner, P. Macha, O. V. Astafiev, E. Il ichev, M. Grajcar, U. Hübner, B. I. Ivanov, P. Neilinger, and H.-G. Meyer, Phys. Rev. Lett. 110, 053602 (2013). 10 6/3/15
Qubit Lasing: Dressed State Lasing Dressed State Lasing: G. Oelsner, P. Macha, O. V. Astafiev, E. Il ichev, M. Grajcar, U. Hübner, B. I. Ivanov, P. Neilinger, and H.-G. Meyer, Phys. Rev. Lett. 110, 053602 (2013). 11 6/3/15
Quantum Heat Enging and Lasing Creating photon in the resonator by using the heat flow from a hot resistor with temperature to a cold resistor with temperature This problem is very similar, to problems discussed for quantum heat engines. Noah Linden, Sandu Popescu, and Paul Skrzypczyk, Phys. Rev. Lett. 105, 130401 (2010) 12 6/3/15
Quantum Heat Enging and Lasing Most likely the energy flows to the cold bath, both from the hot resistor and from the resonator. However, we need the energy to flow from hot resistor to cold resistor and oscillator. Heat flows from hot to cold: 13 6/3/15 Lasing:
Quantum Heat Enging and Lasing Temperatures: Both resistors have ohmic spectra with a RC-cut-off frequency: M. Marthaler, Y. Utsumi, D. S. Golubev, A. Shnirman, G. Schön, Phys. Rev. Lett. 107, 093901 (2011) 14 6/3/15
Quantum Heat Enging and Lasing Simple case: Replacing the resistors with resonators with a low Q-factor. 15 6/3/15
Quantum metamaterials Pascal Macha, Gregor Oelsner, Jan-Michael Reiner,, Stephan Andre, Gerd Schön, Uwe Hubner, HansGeorg Meyer, Evgeni Il ichev and Alexey V. Ustinov, Nat. Comm. 5, 5146 (2014). 16 6/3/15
Quantum metamaterials We model lasing, by allowing for some process which creates population inversion: 17 6/3/15
Quantum metamaterials Equation of motion for the system: 18 6/3/15
Quantum metamaterials: Disorder A closed equation for the photon number can be derived: 19 6/3/15
Quantum metamaterials: Disorder A closed equation for the photon number can be derived: 20 6/3/15
Quantum metamaterials: Disorder A closed equation for the photon number can be derived: 21 6/3/15
Lasing with a disordered quantum metamaterials 22 6/3/15
Lasing with a disordered quantum metamaterials 23 6/3/15
Lasing with a disordered quantum metamaterials 24 6/3/15
Lasing with a disordered quantum metamaterials 25 6/3/15
Conclusion 26 6/3/15
27 6/3/15
Outline 1. The description of the Josephson Junction array 2. Charge transport at small voltages Color coded: Fourier transform of 3. The parity effect 4. The parity effect in arrays 5. Results J. Bylander, T. Duty, P. Delsing, Nature 434, 361 (2005) Charge leaves the array with frequency 28 6/3/15
The description of the JJ array The minimal model of the Josephson array: Color coded: Fourier transform of Small islands coupled by tunnel junctions: J. Bylander, T. Duty, P. Delsing, Nature 434, 361 (2005) Charge leaves the array with frequency 29 6/3/15
The description of the JJ array Charge noise could act on the island and many more noise sources coupled couple to the array: Color coded: Fourier transform of J. H. Cole, J. Leppäkangas, M. Marthaler, New. J. Phys. 16, 015015 (2014) Small islands coupled by tunnel junctions: J. Bylander, T. Duty, P. Delsing, Nature 434, 361 (2005) Charge leaves the array with frequency 30 6/3/15
The description of the JJ array Charge noise could act on the island and many more noise sources coupled couple to the array: Color coded: Fourier transform of Small islands coupled by tunnel junctions: J. Bylander, T. Duty, P. Delsing, Nature 434, 361 (2005) Charge leaves the array with frequency 31 6/3/15
The description of the JJ array For large tunneling resistance the Josephson tunneling can be neglected. Small islands coupled by tunnel junctions: Quasiparticle Tunneling: Cooper-Pair Tunneling: 32 6/3/15