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Title Heisenberg-Langevin Formalism for Open Circuit-QED Systems
Publication Date
Date Accessioned
Degree PhD
Degree Level doctoral
University/Publisher Princeton University
Abstract We present a Heisenberg-Langevin formalism to study the effective dynamics of a superconducting qubit coupled to an open multimode resonator, without resorting to the rotating wave, two level, Born or Markov approximations. Our effective equations are derived by eliminating resonator degrees of freedom while encoding their effect in the Green's function of the electromagnetic background. We account for the openness of the resonator exactly by employing a spectral representation for the Green's function in terms of a set of non-Hermitian modes. A well-behaved time domain perturbation theory is derived to systematically account for the nonlinearity of weakly nonlinear qubits like transmon. We apply this method to the problem of spontaneous emission, capturing accurately the non-Markovian features of the qubit dynamics, valid for any qubit-resonator coupling strength. Any discrete-level quantum system coupled to the electromagnetic continuum is subject to radiative decay and renormalization of its energy levels. When inside a cavity, these quantities can be strongly modified with respect to vacuum. Generally, this modification can be captured by including only the closest resonant cavity mode. In circuit QED architecture, with substantial coupling strengths, it is however found that such rates are strongly influenced by far off-resonant modes. A multimode calculation over the infinite set of cavity modes leads to divergences unless an artificial cutoff is imposed. Previous studies have not pointed out what the source of this divergence is. Quite interestingly, the renormalization of spectrum is mutual, i.e. the electromagnetic modal structure of the cavity is also modified due to scattering by the atom. In cavity QED, this phenomenon is manifested as a diamagnetic term, known as the $A^2$ contribution. We show that unless the effect of $A^2$ is accounted for up to all orders exactly, any multimode calculations of circuit QED quantities is bound to diverge. Subsequently, we present the calculation of finite radiative corrections to qubit properties that is free of an artificially introduced high frequency cut-off.
Subjects/Keywords Cavity-QED; Circuit-QED; Heisenberg-Langevin; Lamb Shift; Quantum Optics; Spontaneous Emission
Contributors Tureci, Hakan E (advisor)
Language en
Country of Publication us
Record ID oai:dataspace.princeton.edu:88435/dsp01ff3657916
Repository princeton
Date Retrieved
Date Indexed 2020-10-21
Issued Date 2017-01-01 00:00:00

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…decay rate and the Lamb shift using our Heisenberg-Langevin framework. The transmission |T |2 is shown versus the real frequency for the bare resonator modes (solid black curves). Capacitive coupling to the qubit, whose transition frequency ωj…

…cavity quantum electrodynamics, summarize the models commonly used to describe these systems and discuss their advantages and limitations. In chapter 3, we introduce our first principles Heisenberg-Langevin formalism, which does not employ rotating wave…

…137 A.2.2 Classical Hamiltonian and Heisenberg equations of motion in the continuum limit . . . . . . . . . . . . . . . . . . . . . . . . 138 A.3 Modified resonator eigenmodes and eigenfrequencies . . . . . . . . . . 141 B Unitless quantum equations of…

…motion for an open cQED system 144 C Effective dynamics of the transmon via a Heisenberg picture Green’s function method 149 C.1 Definition of G(x, t|x0 , t0 ) . . . . . . . . . . . . . . . . . . . . . . . . . 150 C.2 Spectral representation…