Macroscopic Quantum Coherence

Macroscopic quantum coherence is the persistence of quantum coherence in a system involving many particles or a collective, experimentally accessible degree of freedom. The term has two related uses: extended phase coherence in systems such as superconductors and condensates, and coherence between macroscopically distinguishable states, such as opposite circulating currents in a superconducting loop. The latter concerns whether quantum superposition remains observable beyond microscopic systems. These meanings should not be treated as identical. (nature.com)

Coherence and macroscopicity

In quantum mechanics, coherence describes phase relationships that allow alternatives to produce interference. For two approximately orthogonal collective states, $|A\rangle$ and $|B\rangle$ , a coherent state can be written as

|\psi\rangle=\alpha|A\rangle+\beta|B\rangle, \qquad |\alpha|^2+|\beta|^2=1.

Its density matrix contains off-diagonal terms proportional to $\alpha\beta^*$ . An incoherent statistical mixture with the same populations lacks these terms. Consequently, measuring only how often the system occupies each alternative does not establish coherence: measurements must also distinguish the superposition from the corresponding mixture. (people.physics.illinois.edu)

“Macroscopic” does not have a universal threshold defined by size, mass, or particle number. Relevant criteria include the number of constituents involved and the distinguishability of the superposed alternatives through a collective observable. A large physical object can exhibit quantum behavior in only one selected degree of freedom, without all its internal motions forming a coherent superposition. (people.physics.illinois.edu)

Collective phase coherence

In condensed-matter physics, collective coherence is often described by a complex order parameter, conventionally written

\Psi(\mathbf r)=|\Psi(\mathbf r)|e^{i\theta(\mathbf r)}.

The phase $\theta$ describes relationships between different regions of the system. This macroscopic description is not generally the complete many-particle wave function. Extended phase order, familiar from superconductivity, superfluidity, and Bose–Einstein condensates, does not by itself establish a superposition of two macroscopically distinct configurations. (homepages.physik.uni-muenchen.de)

In conventional superconductors, the collective state involves Cooper pairs. The Josephson effect makes relative phase experimentally accessible: a current can flow between superconductors separated by a weak link, with its magnitude depending on their phase difference. In a Josephson junction, this collective phase can also serve as a dynamical quantum coordinate. (people.umass.edu)

Condensate coherence can be investigated by overlapping expanding atomic clouds. In 1997, researchers observed high-contrast matter-wave interference between two sodium condensates. The fringes provided evidence of spatial coherence and long-range correlations, rather than merely showing that many atoms occupied a low-energy state. (homepages.physik.uni-muenchen.de)

Superpositions of collective states

Superconducting circuits provide a particularly controlled setting for studying coherence between distinguishable collective alternatives. A superconducting loop interrupted by a Josephson junction can have states associated with different magnetic fluxes and circulating currents. Near suitable operating points, quantum coupling produces superpositions of these alternatives. (nature.com)

In 2000, Jonathan R. Friedman and colleagues reported spectroscopic evidence for superpositions of distinct flux states in a superconducting quantum interference device (SQUID). The observed energy-level structure agreed with a model in which states associated with different potential wells were coherently coupled. This was evidence from spectroscopy, not a direct observation of an everyday-sized object occupying two visible positions. (nature.com)

Coherent control of circuit states subsequently became central to superconducting qubits. In 2004, researchers demonstrated controlled coupling between a flux qubit and an oscillator formed by a SQUID circuit, using microwave spectroscopy and coherent oscillations to investigate their coupled dynamics. (nature.com)

Distinction from macroscopic quantum tunneling

Macroscopic quantum tunneling occurs when a collective coordinate crosses a potential barrier through a quantum process. Such tunneling can occur without a persistent, experimentally detectable phase relationship between the initial and final alternatives. Observing escape from a metastable state therefore does not automatically demonstrate macroscopic quantum coherence. Coherence requires additional evidence that distinguishes coherent coupling or evolution from incoherent transitions. (people.umass.edu)

Decoherence and experimental significance

Quantum decoherence arises when interactions correlate a system’s alternatives with distinguishable environmental states. When the environment is not measured, interference between those alternatives becomes suppressed in the system’s reduced density matrix. Environmental noise and uncontrolled coupling therefore limit the preparation, preservation, and detection of collective superpositions. Decoherence explains loss of observable interference; it is not, by itself, a complete resolution of the quantum measurement problem. (arxiv.org)

Experiments on macroscopic coherence test how far quantum predictions apply to collective systems and provide methods for preparing and manipulating quantum information. They also demonstrate that coherence and quantum entanglement are related but distinct: coherence concerns superposed alternatives in a specified basis, whereas entanglement concerns nonseparable states of multiple subsystems. A coherent circuit state need not be entangled with another system, although controlled coupling can generate such entanglement. (nature.com)

References

Testing the limits of quantum mechanics: motivation, state of play, prospectspeople.physics.illinois.edu
Observation of Interference Between Two Bose Condensateshomepages.physik.uni-muenchen.de
Quantum superposition of distinct macroscopic statesnature.com
Quantum superposition of distinct macroscopic statespeople.umass.edu
Coherent dynamics of a flux qubit coupled to a harmonic oscillatornature.com
Decoherence and the transition from quantum to classical -- REVISITEDarxiv.org