Document Type : Full length research Paper

**Abstract**

In this paper, we study multilevel multi-photon resonances in a strongly driven four-level quantum system, where one level is periodically swept through other levels with constant energy separation E and 2E. Near the multi-photon resonance conditions, we find qualitatively different behavior for the number of even or odd photons. We explain this phenomenon in terms of families of interfering trajectories of the multilevel system. For beginning our detailed analysis based on a perturbative treatment in terms of the small parameters that characterize the strong driving limit, we introduce the strong-dephasing regime that is modeled by Gaussian white-noise fluctuations on each of the unperturbed energy levels. Within this model we calculate the rates of inter-level transitions, working up to fourth order in the couplings. Finally, we connect our results to the experiments in which current through spin-blockaded double quantum dots was measured in the presence of strong ac driving. The setup can be relevant for a variety of solid state and atomic or molecular systems. In particular, it provides a clear mechanism to explain recent puzzling experimental observations in strongly driven double quantum dots.

**Keywords**

- Quantum dot
- Interference phase
- Strong dephasing regime
- Transition rate
- Multi-level interference resonances

**Main Subjects**

[1] M. Mark, F. Ferlaino, S. Knoop, J.G. Danzl, T. Kraemer, C. Chin, H.-C. Nägerl, R. Grimm, Spectroscopy of ultracold trapped cesium Feshbach molecules, *Physical Review* *A* *76* (2007) 042514.

[2] F. Lang, P.V.D. Straten, B. Brandsttter, G. Thalhammer, K. Winkler, P.S. Julienne, R. Grimm, J. Hecker Denschlag, Cruising through molecular bound state manifolds with radio frequency, *Nature* *Physics* *4* (2008) 223.

[3] W.D. Oliver, Y. Yu, J.C. Lee, K.K. Berggren, L.S. Levitov, T.P. Orlando, Mach-Zehnder interferometry in a strongly driven superconducting qubit, *Science* *310* (2005) 1653.

[4] X-M. Tong, S-I. Chu, Time-dependent density-functional theory for strong-field multiphoton processes: Application to the study of the role of dynamical electron correlation in multiple high-order harmonic generation, *Physical Review* *A* *57* (1998) 452.

[5] F.H.M. Faisal, *Theory of Multiphoton Processes*, Plenum, New York, (1987).

[6] G. Casati, L. Molinari, Quantum Chaos with Time-Periodic Hamiltonians, *Progress of Theoretical Physics Supplement* *98* (1989) 287; G. Casati, B.V. Chirikov, D.L. Shepelyansky, I. Guaneri, Relevance of classical chaos in quantum mechanics: The hydrogen atom in a monochromatic field, *Physics Reports* *154* (1987) 77-123.

[7] A.G. Fainshtein, N.L. Manakov, V.D. Ovsiannikov, L.P. Rapoport, Nonlinear susceptibilities and light scattering on free atoms, *Physics Reports* *210*(1992) 111-221.

[8] M. Kleber, Exact solutions for time-dependent phenomena in quantum mechanics, *Physics Reports* *236* (1994) 331-393.

[9] S. Ashhab, J.R. Johansson, A.M. Zagoskin, F. Nori, Two-level systems driven by large-amplitude fields, *Physical Review* *A* *75* (2007) 063414.

[10] S.N. Shevchenko, S. Ashhab, F. Nori, Landau-Zener-Stückelberg interferometry, *Physics Reports* *492* (2010) 1-30.

[11] H. Ribeiro, J.R. Petta, G. Burkard, Interplay of charge and spin coherence in Landau- Zener- Stückelberg- Majorana interferometry, *Physical Review* *B* *87* (2013) 235318.

[12] J. Stehlik, Y. Dovzhenko, J.R. Petta, J.R. Johansson, F. Nori, H. Lu, A.C. Gossard, Landau-Zener-Stückelberg interferometry of a single electron charge qubit, *Physical Review* *B* *86* (2012) 121303.

[13] J. Zhou, P. Huang, Q. Zhang, Z. Wang, T. Tan, X. Xu, F. Shi, X. Rong, S. Ashhab, J. Du, Observation of Time-domain Rabi oscillations in the Landau-Zener regime with a single electronic spin, *Physical Review Letters* *112* (2014) 010503.

[14] M.O. Scully, M.S. Zubairy, *Quantum Optics* (Cambridge University Press, Cambridge, England, (1997).

[15] G. Sun, X. Wen, B. Mao, J. Chen, Y. Yu, P. Wu, and S. Han, Tunable quantum beam splitters for coherent manipulation of a solid-state tripartite qubit system, *Nature Communications *1, *51* (2010).

[16] D.M. Berns, M.S. Rudner, S.O. Valenzuela, K.K. Berggren, W.D. Oliver, L.S. Levitov, T.P. Orlando, Nature (London) **455** (2008) 51.

[17] G. Sun, X. Wen, Y. Wang, S. Cong, J. Chen, L. Kang, W. Xu, Y. Yu, S. Han, P. Wu, Population inversion induced by Landau-Zener transition in a strongly driven rf-SQUID, *Applied Physics **Letters* *94* (2009) 102502.

[18] J.I. Colless, X.G. Croot, T.M. Stace, A.C. Doherty, S.D. Barrett, H. Lu, A.C. Gossard, D.J. Reilly, Raman phonon emission in a driven double quantum dot,* Nature Communications* *5* (2014) 3716.

[19] S.O. Valenzuela, W.D. Oliver, D.M. Berns, K.K. Berggren, L.S. Levitov, T.P. Orlando, Microwave-induced cooling of a superconducting qubit, *Science* *314* (2006) 1589.

[20] E.A. Laird, C. Barthel, E.I. Rashba, C.M. Marcus, M.P. Hanson, A.C. Gossard, A new mechanism of electric dipole spin resonance: hyperfine coupling in quantum dots, *Semiconductor **Science and Technology* *24* (2009) 064004.

[21] J. Stehlik, M.D. Schroer, M.Z. Maialle, M. H. Degani, J.R. Petta, Extreme harmonic generation in electrically driven spin resonance, *Physical Review Letters* *112* (2014) 227601.

[22] E.I. Rashba, Mechanism of half-frequency electric dipole spin resonance in double quantum dots: Effect of nonlinear charge dynamics inside the singlet manifold, *Physical Review* *B* *84* (2011) 241305.

[23] G. Széchenyi, A. Pályi, Maximal Rabi frequency of an electrically driven spin in a disordered magnetic field, *Physical Review* *B* *89* (2014) 115409.

[24] M.P. Nowak, B. Szafran, F.M. Peeters, Resonant harmonic generation and collective spin rotations in electrically driven quantum dots, *Physical Review* *B* *86* (2012) 125428.

[25] J. Stehlik, M.D. Schroer, M.Z. Maialle, M. H. Degani, J.R. Petta, Extreme harmonic generation in electrically driven spin resonance, *arXiv*: 1312.3875v1.

[26] J. Danon, Mark S. Rudner, Multilevel interference resonances in strongly driven three-level systems, *Physical Review Letters* *113* (2014) 247002.

[27] H. Sambe, Steady states and quasienergies of a quantum-mechanical system in an oscillating field, *Physical Review* *A* *7* (1973) 2203.

[28] S. Kohler, J. Lehmann, P. Hänggi, Driven quantum transport on the nanoscale, *Physics Reports* *406* (2005) 379-443.

[29] V.P. Krainov, Sov. Theory of resonance multiphoton transitions in a three-level system under the influence of a strong electromagnetic field, *Journal of Experimental and Theoretical Physics* *43* (1976) 622.

[30] K.C. Nowack, F.H.L. Koppens, Y.V. Nazarov, L.M.K. Vandersypen, Coherent control of a single electron spin with electric fields, *Science* *318* (2007) 1430.

[31] E.A. Laird, C. Barthel, E.I. Rashba, C.M. Marcus, M.P. Hanson, A.C. Gossard, Hyperfine-mediated gate-driven electron spin resonance, *Physical Review Letters* *99* (2007) 246601.

October 2018

Pages 105-117

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**Receive Date:**23 February 2017**Revise Date:**13 March 2018**Accept Date:**22 May 2018