Macroscopic Quantum Tunneling

Macroscopic quantum tunneling (MQT) is quantum tunneling involving a collective variable of a many-particle system, rather than merely the position of an individual particle. A prominent example is the escape of the superconducting phase difference in an electrical circuit from a metastable potential well. The phenomenon demonstrates that quantum mechanics can govern variables ordinarily described by macroscopic circuit theory, including phase, current, and magnetic flux. Here “macroscopic” refers to the collective nature of the variable, not necessarily to a large object moving through a physical wall. (physics.umd.edu)

Physical meaning

In classical mechanics, a system confined within a potential well cannot cross its surrounding barrier unless it acquires sufficient energy. Quantum mechanically, a state can extend into a classically forbidden region, giving a nonzero probability of passage through the barrier. For MQT, the coordinate describing this passage represents the organized behavior of many microscopic constituents. (physics.umd.edu)

Superconductivity provides an especially useful setting. Many Cooper pairs participate in a condensate characterized by a common phase. The phase difference between two superconductors can therefore act as a collective dynamical coordinate. Its tunneling is distinct from the microscopic transfer of pairs through the insulating layer responsible for the Josephson effect: the former concerns escape through a barrier in the circuit’s effective potential, whereas the latter supplies the coupling that helps create that potential. (physics.umd.edu)

Josephson-junction description

A current-biased Josephson junction is a standard experimental realization. Its phase difference, $\phi$, behaves mathematically like the position of a particle in a tilted periodic potential:

Here $I$ is the applied current, $I_c$ the critical current, $e$ the elementary electric charge, and $\hbar$ the reduced Planck constant. Junction capacitance supplies the effective inertia. Below the critical current, the potential contains local minima separated by barriers; increasing the bias tilts the potential further and lowers the escape barrier. This is commonly called the “tilted washboard” description. (harvest.aps.org)

When the phase remains trapped in a well, its average time derivative vanishes and the junction has zero average voltage. Escape allows the phase to evolve, producing a measurable voltage. In an underdamped junction, this transition can register as a switch into a persistent finite-voltage state. The experiment consequently detects tunneling of a collective coordinate through an electrical signal, rather than observing the motion of each participating electron. (harvest.aps.org)

Thermal activation and quantum escape

Two mechanisms can produce escape from a metastable well. In thermal activation, fluctuations provide enough energy to pass over the barrier. Its rate generally contains an exponential factor of the form

where $\Delta U$ is the barrier height, $T$ the temperature, and $k_B$ Boltzmann’s constant. Quantum escape instead occurs through the barrier, with a rate controlled by the barrier profile, effective inertia, and environmental coupling. (harvest.aps.org)

As temperature decreases, thermal escape becomes less frequent and tunneling can dominate. A low-temperature escape rate that approaches a temperature-independent value is an important signature, but convincing identification also requires independently measured circuit parameters and exclusion of unintended excitation. Microwave-induced transitions provide complementary information about the well’s internal dynamics and quantized energy levels. (journals.aps.org)

Experimental development

In 1985, Michel H. Devoret, John M. Martinis, and John Clarke reported quantitative measurements of escape from the zero-voltage state of an underdamped, current-biased Josephson junction. They determined relevant junction parameters in the thermal regime, including through resonant activation by microwaves. At low temperatures, the escape rate became temperature independent and agreed with the predicted zero-temperature tunneling rate without adjustable parameters. Their paper appeared on October 28, 1985. (journals.aps.org)

A companion experiment, published on October 7, 1985, demonstrated discrete energy levels associated with the junction’s phase difference. Microwave excitation increased escape when its frequency matched transitions between levels. Such spectroscopic evidence distinguished quantum level structure from an account based solely on classical fluctuations. The measured level positions agreed quantitatively with calculations using parameters established in the classical regime. (harvest.aps.org)

The 2025 Nobel Prize in Physics was awarded jointly to Clarke, Devoret, and Martinis for discovering macroscopic quantum mechanical tunneling and energy quantization in an electric circuit. (nobelprize.org)

Environment and related phenomena

A macroscopic coordinate is coupled to other degrees of freedom. Their influence cannot always be represented simply by adding classical noise. The Caldeira–Leggett model established a framework for treating environmental coupling and quantum dissipation. Caldeira and Anthony Leggett’s 1981 analysis showed how dissipative coupling modifies—and, under its stated assumptions, suppresses—escape by tunneling from a metastable state. (journals.aps.org)

MQT must also be distinguished from macroscopic quantum coherence. Escape from a metastable well establishes quantum barrier penetration, but does not by itself demonstrate sustained coherent oscillations between macroscopically distinct configurations. Environmental dissipation can suppress coherence as well as alter tunneling dynamics. (journals.aps.org)

Related collective dynamics occur in a superconducting quantum interference device, where magnetic-flux configurations can occupy different potential minima. Theory describes microwave-driven transitions between fluxoid states and the influence of damping on their quantum dynamics. (journals.aps.org)

Connection to quantum circuits

The ability to quantize collective circuit variables helped establish the physical basis of the superconducting qubit. Josephson circuits can be engineered to possess controllable, non-equally spaced quantum levels suitable for information processing. However, useful qubit operation requires control and preservation of quantum states, not merely observation of irreversible escape. Macroscopic tunneling and circuit energy quantization are foundational demonstrations underlying this development, rather than interchangeable descriptions of every superconducting-qubit design. (physics.umd.edu)