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arXiv:0905.3674 · Physical Review B

Dressed relaxation and dephasing in a strongly driven two-level system

Christopher M. Wilson, Göran Johansson, T. Duty, Fredrik Persson, Martin Sandberg, Per Delsing

Published Jan 29, 2010• 73 citations
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Abstract

We study relaxation and dephasing in a strongly driven two-level system interacting with its environment. We develop a theory which gives a straightforward physical picture of the complex dynamics of the system in terms of dressed states. In addition to the dressing of the energy diagram, we describe the dressing of relaxation and dephasing. We find a good quantitative agreement between the theoretical calculations and measurements of a superconducting qubit driven by an intense microwave field. The competition of various processes leads to a rich structure in the observed behavior, including signatures of population inversion.

DOI
10.1103/physrevb.81.024520

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We study relaxation and dephasing in a strongly driven two-level system interacting with its environment. We develop a theory which gives a straightforward physical picture of the complex dynamics of the system in terms of dressed states. In addition to the dressing of the energy diagram, we describe the dressing of relaxation and dephasing. We find a good quantitative agreement between the theoretical calculations and measurements of a superconducting qubit driven by an intense microwave field. The competition of various processes leads to a rich structure in the observed behavior, including signatures of population inversion.
The coherent dynamics of relaxing spin qubits driven by a classical bichromatic field comprising a strong resonant component and a weaker component with a frequency close to the strong-field Rabi frequency is studied. The double dressing by the bichromatic field modifies dephasing and dissipation processes. We demonstrate that detuning of the weaker-field frequency from the strong-field Rabi frequency prolongs the decay of Rabi oscillations between some doubly dressed states. The sensitivity of Rabi oscillations to the modified detuning-dependent relaxation is illustrated for nitrogen-vacancy qubits in diamond. We discuss a steady-state population inversion of the doubly dressed-state levels.
We measure longitudinal dressed states of a superconducting qubit, the single Cooper-pair box, and an intense microwave field. The dressed states represent the hybridization of the qubit and photon degrees of freedom and appear as avoided level crossings in the combined energy diagram. By embedding the circuit in an rf oscillator, we directly probe the dressed states. We measure their dressed gap as a function of photon number and microwave amplitude, finding good agreement with theory. In addition, we extract the relaxation and dephasing rates of these states.
A superconducting qubit was driven in an ultrastrong fashion by an oscillatory microwave field, which was created by coupling via the nonlinear Josephson energy. The observed Stark shifts of the "atomic" levels are so pronounced that corrections even beyond the lowest-order Bloch-Siegert shift are needed to properly explain the measurements. The quasienergies of the dressed two-level system were probed by resonant absorption via a cavity, and the results are in agreement with a calculation based on the Floquet approach.
Interaction between quantum two-level systems (qubits) and electromagnetic fields can provide additional coupling channels to qubit states. In particular, the interwell relaxation or Rabi oscillations, resulting, respectively, from the multi- or single-mode interaction, can produce effective crossovers, leading to electromagnetically induced interference in microwave driven qubits. The environment is modeled by a multimode thermal bath, generating the interwell relaxation. Relaxation induced interference, independent of the tunnel coupling, provides deeper understanding to the interaction between the qubits and their environment. It also supplies a useful tool to characterize the relaxation strength as well as the characteristic frequency of the bath. In addition, we demonstrate the relaxation can generate population inversion in a strongly driving two-level system. On the other hand, different from Rabi oscillations, Rabi-oscillation-induced interference involves more complicated and modulated photon exchange thus offers an alternative means to manipulate the qubit, with more controllable parameters including the strength and position of the tunnel coupling. It also provides a testing ground for exploring nonlinear quantum phenomena and quantum state manipulation in qubits either with or without crossover structure.
We experimentally and theoretically study the frequency shift of a driven cavity coupled to a superconducting charge qubit. In addition to previous studies, here we also consider drive strengths large enough to energetically allow for quasiparticle creation. Quasiparticle tunnelling leads to the inclusion of more than two charge states in the dynamics. To explain the observed effects, we develop a master equation for the microwave dressed charge states, including quasiparticle tunnelling. A bimodal behaviour of the frequency shift as a function of gate voltage can be used for sensitive charge detection. However, at weak drives, the charge sensitivity is significantly reduced by nonequilibrium quasiparticles, which induce transitions to a non-sensitive state. Unexpectedly, at high-enough drives, the quasiparticle tunnelling enables a very fast relaxation channel to the sensitive state. In this regime, the charge sensitivity is thus robust against externally injected quasiparticles and the desired dynamics prevail over a broad range of temperatures. We find very good agreement between the theory and experiment over a wide range of drive strengths and temperatures.
Two-level systems (TLS) are widely recognized as a dominant source of energy relaxation in superconducting qubits, limiting coherence times and device performance. While TLS-induced dissipation is often modeled as independent channels, interacting TLS can form finite many-body environments whose dynamical role in qubit relaxation remains insufficiently understood. Building on the information-erasure-based framework for irreversible thermalization developed in our previous work, we present a microscopic model and numerical simulations of a superconducting qubit coupled to a finite interacting many-body TLS environment as a concrete physical realization of this mechanism. We show that effective irreversible energy relaxation can emerge from intrinsic many-body dynamics without invoking external baths or phenomenological dissipation. The introduction of information erasure drives a transition from coherent oscillatory energy exchange to nonoscillatory exponential relaxation of the qubit. The relaxation times exhibit the scaling T1,T2∝Jq,τ−2T_1, T_2 \propto J_{q,τ}^{-2}T1​,T2​∝Jq,τ−2​ with respect to the qubit-TLS coupling strength, consistent with Fermi's golden rule and Lindblad-type descriptions. Importantly, both exponential decay and its scaling behavior arise directly from microscopic many-body dynamics. These results provide quantitative insight into TLS-induced decoherence mechanisms and establish a microscopic link between information erasure, many-body thermalization, and irreversible relaxation in superconducting quantum systems.