Collapse and revival of “Schrödinger cat” states

Abstract

We study the dynamics of the Jaynes-Cummings Model for an array of Nq two level systems (or qubits) interacting with a quantized single mode electromagnetic cavity (or quantum bus). For an initial cavity coherent state |α and the qubit system in a specified 'basin of attraction' in its Hilbert space, we demonstrate the oscillation of a superposition of two macroscopic quantum states between the qubit system and the field mode. From the perspective of either the qubit or the field system, there is collapse and revival of a 'Schrödinger Cat' state.Quantum superposition of macroscopically different states of matter are of fundamental conceptual interest in many fields of physics such as Measurement Theory [1], Quantum Optics [2], Macroscopic Quantum Tunnelling [3] and Quantum Computation [4]. Many of the relevant experiments revolve around the preparation of and measurement on a specific class of states called 'Schrödinger Cat' states [5]. These are quantum superpositions of states which correspond to two (or more) different values of a macroscopic variable, such as the magnetization or the electric field in the cases of a large spin cluster, or large photon number or phase in a cavity mode. In this letter we report the surprising discovery that in a Jaynes-Cummings model (JCM), which describes an array of two-level systems (qubits) interacting with a single cavity mode, the time evolution can be such that sometimes the radiation field and sometimes the qubit subsystem is in a 'Schrödinger Cat' state. In other words, a superposition of macroscopically different states can shift from one set of physical variables to another, as a function of time.The quantum dynamics of two-level systems (qubits), coupled to a single mode of an electromagnetic cavity, arise in many different physically interesting systems. These include Rydberg atoms [5], NMR studies of atomic nuclei [6,7], Cooper Pair Boxes [8], Cavity Quantum Electrodynamics [9], trapped ions [10] and Quantum Computing [4]. A very general and simple Hamiltonian that captures the relevant physics in all these fields is the JCM [11] (for one qubit) and its generalization for multiqubit systems by Tavis and Cummings [12]. Thus, our results are pertinent to a broad range of physical systems.One of the most interesting and surprising predictions of the JCM is the 'collapse and revival' of Rabi oscillations of the occupation probabilities for various qubit states as the system evolves, from an initial state which is a product of a coherent state |α for the radiation field, and a generic qubit state ψ Nq [2], where N q is the number of qubits. These remarkable dynamics occur only because both the matter and the cavity field are treated fully quantum mechanically. Indeed, our aim here is to study the 'collapse and revival' of 'Schrödinger cat'-like states in a multi-qubit subsystem, as well as in the cavity field .For clarity let us specify the multi-qubit JCM Hamiltonian, where each qubit labelled i has ground (excited) state |g i (|e i ) with energy ǫ g,i (ǫ e,i ). Up to...

Towards a complete and continuous Wigner function for an ensemble of spins or qubits

“…[4,5] and the spin Husimi Q functions we refer the reader to Refs. [10,34]. We also note that unlike our function the spin Husimi Q function and the spin Wigner functions of Refs.…”

“…[32][33][34]). The spin versions of these Husimi Q functions have a similar limitation to those of the continuous case.…”

Collapse and revival oscillation in Double Jaynes–Cummings model

“…where, E 0 n A ,n B = (n A + 1 2 )ω A + (n B + 1 2 )ω B and R n i = Ω n i + ω i , respectively. The appearance of multiple number of dressed states due to the entanglement-induced dressing has put our treatment of dressed state formalism in a advantageous position compare to other approaches of D-JCM 21,24,[26][27][28][29][30][31] .…”

Photon echoes for a system of large negative spin and few photons

“…To continue the examination of characteristic times, we next consider the case of 2 TLMs with reference to [29] interacting with the coherent density matrix. Again we assume that the initial photon distribution is coherent with a LMPN.…”

“…Entanglement of TLMs with the quantized field have been discussed by numerous authors in terms of entropy (12,13,29,(32)(33)(34)(35). In general the authors relate entanglement to the Von Neumann entropy defined as with being the density matrix for the system.…”