Entanglement generated by the dispersive interaction: The dressed coherent state

Abstract

In the dispersive regime of qubit-cavity coupling, classical cavity drive populates the cavity, but leaves the qubit state unaffected. However, the dispersive Hamiltonian is derived after both a frame transformation and an approximation. Therefore, to connect to external experimental devices, the inverse frame transformation from the dispersive frame back to the lab frame is necessary. In this work, we show that in the lab frame the system is best described by an entangled state known as the dressed coherent state, and thus even in the dispersive regime, entanglement is generated between the qubit and the cavity. Also, we show that further qubit evolution depends on both the amplitude and phase of the dressed coherent state, and use the dressed coherent state to calculate the measurement contrast of a recently developed dispersive readout protocol.The interaction between a two level system (TLS) and quantized electromagnetic radiation has been studied extensively since the beginnings of quantum mechanics, with much effort devoted to the study of physical systems described by the Jaynes-Cummings Hamiltonian [1]. Over the last few decades the fields of cavity quantum electrodynamics (CQED) and more recently circuit quantum electrodynamics (cQED) have significantly developed, allowing for the exploration of the Jaynes-Cummings interaction in a wide range of parameter regimes and physical systems. In particular in cQED, both the strong coupling regime (g κ, γ, first achieved in Rydberg atoms [2]) and the strong dispersive regime (χ κ, γ) have been reached within the last decade [3]. In cQED, a superconducting qubit serves as the TLS, while the quantized electromagnetic fields are microwaves in either a strip-line resonator or 3D microwave cavity.Contemporary experiments in cQED often work in the strong dispersive regime, where the qubit and microwave cavity are off resonance, and the Jaynes-Cummings interaction reduces to an effective second order shift in system eigen-energies. In this regime, a wide range of quantum information protocols has been demonstrated [4], including quantum teleportation [5], entanglement generation by measurement and feedback [6,7], non-classical microwave state generation [8], and error correction by stabilization measurements [9].When an empty electromagnetic cavity is driven by classical radiation, the state of the cavity is described quantum mechanically by the coherent state |α , where the complex amplitude α depends on the strength and length of the classical drive. In the dispersive regime of qubit-cavity coupling, when a classical cavity drive is applied the state of the joint system is typically described by the product state a |g |α g + b |e |α e , with no qubitcavity entanglement generated if the qubit is not initially in a superposition state.What is often overlooked is that the state a |g |α g + b |e |α e is an accurate description of the joint system * Electronic address: lcggovia@lusi.uni-sb.de state under the dispersive approximation, which involves a frame transformation ...

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