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Oxford University Press eBooks

Schrödinger's Cat and Leggett's SQUID: Quantum Effects on a Large Scale?

Christopher C. Gerry, Kimberley M. Bruno

Published Feb 21, 2013• 0 citations
Publisher

Abstract

This chapter analyzes the problem of locating the divide between the quantum and classical worlds. It discusses Schrödinger's cat paradox; and Leggett's SQUID (superconducting quantum interference device), that when operated under certain conditions can bring about quantum effects on a fairly large scale. It suggests that superposition states, which are routinely produced in the microworld, are difficult to manufacture in larger-scale systems due to the effects of the environment, i.e., the part of the world directly surrounding the quantum system. For larger-scale systems, such as for the interfering cat states of SQUID, the environment has the effect of destroying the quantum coherence of the superposition state at short times. Quantum coherence for the state of the supercurrents can be maintained in such experiments only for short times. The destruction of quantum coherence is known as decoherence.

DOI
10.1093/acprof:oso/9780199666560.003.0007

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This chapter analyzes the problem of locating the divide between the quantum and classical worlds. It discusses Schrödinger's cat paradox; and Leggett's SQUID (superconducting quantum interference device), that when operated under certain conditions can bring about quantum effects on a fairly large scale. It suggests that superposition states, which are routinely produced in the microworld, are difficult to manufacture in larger-scale systems due to the effects of the environment, i.e., the part of the world directly surrounding the quantum system. For larger-scale systems, such as for the interfering cat states of SQUID, the environment has the effect of destroying the quantum coherence of the superposition state at short times. Quantum coherence for the state of the supercurrents can be maintained in such experiments only for short times. The destruction of quantum coherence is known as decoherence.
One of the many challenges facing those who would build a quantum computer is how to assemble a large enough group of qubits in a way that would permit useful computation. For this, solid state qubits have a clear advantage, and the natural order already present in a superconductor makes superconducting qubits a logical choice. The challenge for these “macroscopic” superconducting qubits is to achieve the required internal coherence between states in a single qubit in the face of interactions with the environment. Results of recent experiments at Stony Brook will be presented that demonstrate one can, in fact, produce a coherent superposition of flux states in SQUIDs (Superconducting Quantum Interference Devices). This coherence in SQUIDs is the strongest test to date of the predictions of quantum mechanics in a macroscopic system, e.g. Schrodinger’s cat.
. It is pointed out that the conclusions drawn from a recent quantum interference experiment with light suggest an operational resolution of the Schrödinger cat paradox. On this occasion in honor of Prof. E.T. Jaynes, we recall that he devoted some of his research efforts to the interpretation of quantum mechanics, which led him to propose several experimental tests. Although the ‘neoclassical’ theory he developed was found not to be confirmed by experiment, it nevertheless played a role in encouraging us to think critically about quantum mechanics and to carry out new experiments. This short contribution is concerned with a well-known quantum problem of interpretation. The quantum paradox known as Schrödinger's cat, in which the cat is cast in a linear superposition of the state of being alive and the state of being dead, has been debated since the beginnings of quantum mechanics. Whereas most physicists are ready to concede the existence of superposition states for a microscopic quantum system like an atom, such states appear to be ruled out for a macroscopic system like a cat by common experience. The question then arises at which level classical concepts take over from quantum mechanical ones. In a very clear and readable discussion of this and other paradoxes Glauber has pointed out that the noise inevitably associated with the amplification process accompanying the measurement of a microscopic system leaves the cat in a mixed state rather than a pure one.
Abstract ‘Quantum matter’ describes how superconductors and superfluids can have properties like those found in the strange quantum world of atoms, electrons, and photons. In quantum theory, properties such as energy cannot have any possible value, but are quantized. Energy comes in discrete lumps. Particles can act like waves, be in more than one place at the same time, and interfere with themselves. The weirdness of quantum theory is captured in the paradox of Schrödinger’s cat, where quantum effects occur on the macroscopic scale. This is realized in a superconductor, where magnetic flux is quantized. Brian Josephson proposed an electrical circuit that is the basis for a Superconducting Quantum Interference Device (SQUID). These devices are of technological significance as they are used in quantum computing, and to make precise measurements of fundamental physical constants and of magnetic field strengths. SQUIDs are now used in metrology, the science of precise measurements, being the basis for the international standard for the volt, the unit of electrical voltage, and are used in quantum computing.
"As a rule, the coupling of a quantum system to an uncontrollable thermal reservoir (a “bath”) gives rise to the system’s decoherence, i.e., the destruction of its unitary coherent evolution [1]. Not less common is the rule that the more complex the quantum system, the more detrimental are the bath effects [2]. Here we point out that the coupling of a complex quantum system to a bath may actually induce advantageous coherent dynamics. Namely, an exact solution for a quantum many-body system characterized by large angular momentum (or spin) that is coupled to a thermal bath reveals a hitherto unexplored general effect: bath-induced effectively nonlinear evolution. This evolution can drive the large-spin system into a macroscopic quantum-superposition (“Schroedinger-cat”) state [3, 4]. Such counter-intuitive bath-induced effects should be observable in various setups on long (Markovian) time scales. They change our perspective of non-classicality in open many-body quantum systems. Namely, the bath may cause rather than impede the formation of distinctly non-classical Schroedinger-cat states, despite their fragility in the presence of a bath [2, 5]."
This paper proposes a quantum measurement framework based on structuralstability theory, aiming to resolve the logical dilemma of the quantum–classicaltransition in Schrödinger’s cat paradox. Traditional quantum mechanics relies onexternal mechanisms such as “observer introduction” or “decoherence” to explainmacroscopic reality, leading to vague ontological commitments. We argue that thefundamental reason macroscopic quantum states cannot maintain coherent superpositions lies in the self-organizing critical behavior constrained by the system’sinternal structural stability. The core mechanism is: when a quantum system couples with a classical measuring device, its Hilbert space representation is forced toproject from a high-dimensional unitary representation onto a low-dimensional classical representation, a process driven by the extremization of a structural stabilityfunctional, not by external observation. We rigorously prove that when the system’sstructural information density exceeds a critical threshold, the quantum superposition state cannot satisfy self-consistency constraints mathematically; the systemmust select a classical eigenstate through an “algebraic filtration” mechanism. Thetheory yields three testable predictions: (1) a microscopic entropy production pulseat the moment of coupling between the measuring device and the quantum system,of order 10−21 J/K; (2) a deviation of the quantum Zeno suppression factor fromstandard quantum mechanical predictions on microsecond scales; (3) a scaling-lawdivergence of the decoherence time of macroscopic superpositions at critical parameters. These effects can be tested in coupled superconductor qubit–mechanicalresonator systems. The framework does not modify unitary evolution, does not relyon many-worlds assumptions, and does not introduce collapse postulates; instead,it transforms the measurement problem into a question of compatibility betweenquantum information structure and geometric–topological constraints.
This chapter is devoted to the physics of cavity quantum electrodynamics (CQED) cats. After a brief reminder about the Schrödinger cat problem in quantum optics, it describes how a single atom interacting with a field made of many photons can leave its quantum imprint on this field, bringing it into a superposition of states with distinct classical attributes. It describes the preparation and detection of these ‘Schrödinger cat’ states. It presents simple decoherence models, which account for their extreme fragility. It describes experimental studies of decoherence, which constitute direct explorations of the quantum-classical boundary. It discusses limitations to the size of these cat states and ways to protect them efficiently against decoherence. Finally, the chapter describes proposals to generate and study non-local cats, superpositions of field states delocalised in two cavities.