The nature of the Lamb shift in weakly-anharmonic atoms: from normal mode splitting to quantum fluctuations

Abstract

When a two level system (TLS) is coupled to an electromagnetic resonator, its transition frequency changes in response to the quantum vacuum fluctuations of the electromagnetic field, a phenomenon known as the Lamb shift. Remarkably, by replacing the TLS by a harmonic oscillator, normal mode splitting leads to a quantitatively similar shift, without taking quantum fluctuations into account. In a weakly-anharmonic system, lying in between the harmonic oscillator and a TLS, the origins of such shifts can be unclear. An example of this is the dispersive shift of a transmon qubit in circuit quantum electrodynamics (QED). Although often referred to as a Lamb shift, the dispersive shift observed in spectroscopy in circuit QED could contain a significant contribution from normal-mode splitting that is not driven by quantum fluctuations, raising the question: how much of this shift is quantum in origin? Here, we treat normal-mode splitting separately from shifts induced by quantum vacuum fluctuations in the Hamiltonian of a weakly-anharmonic system, providing a framework for understanding the extent to which observed frequency shifts can be attributed to quantum fluctuations.

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• Black-box superconducting circuit quantization
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• QuCAT: Quantum Circuit Analyzer Tool in Python
• Superconducting qubits beyond the dispersive regime
• Exact quantization of superconducting circuits
• Photon-number-dependent effective Lamb shift
• Sideband transitions in a two-mode Josephson circuit driven beyond the rotating wave approximation
• Phonon-number resolution of voltage-biased mechanical oscillators with weakly-anharmonic superconducting circuits
• Concurrent Fermionic Simulation Gate