On the correspondence principle : implications from a study of the nonlinear dynamics of a macroscopic quantum device

The recovery of classical nonlinear and chaotic dynamics from quantum systems has long been a subject of interest. Furthermore, recent work indicates that quantum chaos may well be significant in quantum information processing. In this paper, we discuss the quantum to classical crossover of a superconducting quantum interference device (SQUID) ring. Such devices comprise a thick superconducting loop enclosing a Josephson weak link and are currently strong candidates for many applications in quantum technologies. The weak link brings with it a nonlinearity such that semiclassical models of this system can exhibit nonlinear and chaotic dynamics. For many similar systems an application of the correspondence principle together with the inclusion of environmental degrees of freedom through a quantum trajectories approach can be used to effectively recover classical dynamics. Here we show (i) that the standard expression of the correspondence principle is incompatible with the ring Hamiltonian and we present a more pragmatic and general expression which finds application here and (ii) that practical limitations to circuit parameters of the SQUID ring prevent arbitrarily accurate recovery of classical nonlinear dynamics

Delayed creation of entanglement in superconducting qubits interacting with a microwave field

We explore the role played by the intrinsic decoherence in superconducting charge qubits in the presence of a microwave field applied as a magnetic flux. We study how the delayed creation of entanglement, which is opposite to the sudden death of entanglement, can be induced. We compute the time evolution of the population inversion, total correlation and entanglement, taking into account the junction mixed state and dissipation of the cavity field. We show that although decoherence destroys the correlation of the junction and field, information of the initial state may be obtained via quasi-probability distribution functions

Quantum-classical crossover of a field mode

We explore the quantum-classical crossover in the behaviour of a quantum field mode. The quantum behaviour of a two-state system—a qubit—coupled to the field is used as a probe. Collapse and revival of the qubit inversion form the signature for quantum behaviour of the field and continuous Rabi oscillations form the signature for classical behaviour of the field. We demonstrate both limits in a single model for the full coupled system, for field states with the same average field strength, and so for qubits with the same Rabi frequency

On the quantum-to-classical transition of a particle in a box

The exact formulation of the correspondence principle and in particular understanding the quantum-to-classical transition remains an open problem in quantum mechanics. In this paper we present our investigation into the quantumto-classical transition of the most trivial of quantum systems — a particle in a box. Whilst it is perhaps surprising, even this example can produce new physical insight into these fundamental problems. With modern fabrication techniques of nano-mechanical systems we will be able to experimentally investigate these results and directly observe the quantum-to-classical transition. This will enable us to build technologies that probe the fundamental questions of quantum mechanics, such as the maximum size of a quantum object

Quantum systems engineering: a structured approach to accelerating the development of a quantum technology industry

The exciting possibilities in the field of new quantum technologies extend far beyond the well-reported application of quantum computing. Precision timing, gravity sensors and imagers, cryptography, navigation, metrology, energy harvesting and recovery, biomedical sensors and imagers, and real-time optimisers all indicate the potential for quantum technologies to provide the basis of a technological revolution. From the field of Systems Engineering emerges a focused strategy for the development cycle, enabling the existence of hugely complex products. It is through the adoption of systems thinking that the semiconductor industry has achieved massive industrial and economic impact. Quantum technologies rely on delicate, non-local and/or entangled degrees of freedom — leading to great potential, but also posing new challenges to the development of products and industries. We discuss some of the challenges and opportunities regarding the implementation of Systems Engineering and systems thinking into the quantum technologies space

Quantum measurement and the quantum to classical transition in a non-linear quantum oscillator

We study a non-linear quantum mechanical oscillator, acting as a measurement device. Candidate systems for realising such apparatus range from superconducting devices through to nano-mechanical resonators. The measurement device comprises an oscillator circuit where the dynamics of expectation values, in its correspondence limit, are either chaotic-like or periodic depending on the measured state of the quantum object – in this case a qubit. In a previous work we showed how the classical like trajectories of such a quantum system can act as a model of a projective measurement process. Here we investigate the quantum to classical transition of the measurement device and postulate criteria for realisation of an effective implementation of such a device

Overcoming decoherence in the collapse and revival of spin Schrodinger-cat states

In addition to being a very interesting quantum phenomenon, Schrödinger-cat-state swapping has the potential for application in the preparation of quantum states that could be used in metrology and other quantum processing. We study in detail the effects of field decoherence on a Schrödinger-cat-state-swapping system comprising a set of identical qubits, or spins, all coupled to a field mode. We demonstrate that increasing the number of spins actually mitigates the effects of field decoherence on the collapse and revival of a spin Schrödinger-cat state, which could be of significant utility in quantum metrology and other quantum processing

Harmonic mixing in two coupled qubits: Quantum synchronization via ac drives

Simulating a system of two driven coupled qubits, we show that the time-averaged probability to find one driven qubit in its ground or excited state can be controlled by an ac drive in the second qubit. Moreover, off-diagonal elements of the density matrix responsible for quantum coherence can also be controlled via driving the second qubit; that is, quantum coherence can be enhanced by appropriate choice of the biharmonic signal. Such a dynamic synchronization of two differently driven qubits has an analogy with harmonic mixing of Brownian particles forced by two signals through a substrate. Nevertheless, the quantum synchronization in two qubits occurs due to multiplicative coupling of signals in the qubits rather than via a nonlinear harmonic mixing for a classical nanoparticle. Quantum harmonic mixing proposed here can be used to manipulate one driven qubit by applying an additional ac signal to the other qubit coupled with the one we have to control

Visualization of correlations in hybrid discrete—continuous variable quantum systems

In this work we construct Wigner functions for hybrid continuous and discrete variable quantum systems. We demonstrate new capabilities in the visualization of the interactions and correlations between discrete and continuous variable quantum systems, where visualizing the full phase space has proven difficult in the past due to the high number of degrees of freedom. Specifically, we show how to clearly distinguish signatures that arise due to quantum and classical correlations in an entangled Bellcat state. We further show how correlations are manifested in different types of interaction, leading to a deeper understanding of how quantum information is shared between two subsystems. Understanding the nature of the correlations between systems is central to harnessing quantum effects for information processing; the methods presented here reveal the nature of these correlations, allowing a clear visualization of the quantum information present in these hybrid discrete-continuous variable quantum systems. The methods presented here could be viewed as a form of quantum state spectroscopy

Energy downconversion between classical electromagnetic fields via a quantum mechanical SQUID ring

We consider the interaction of a quantum mechanical SQUID ring with a classical resonator (a parallel LC tank circuit). In our model we assume that the evolution of the ring maintains its quantum mechanical nature, even though the circuit to which it is coupled is treated classically. We show that when the SQUID ring is driven by a classical monochromatic microwave source, energy can be transferred between this input and the tank circuit, even when the frequency ratio between them is very large. Essentially, these calculations deal with the coupling between a single macroscopic quantum object (the SQUID ring) and a classical circuit measurement device where due account is taken of the nonperturbative behavior of the ring and the concomitant nonlinear interaction of the ring with this device