Engineered reservoirs help a tiny quantum refrigerator stay colder

A refrigerator built from three quantum bits

How much does a refrigerator’s performance depend on the machine, and how much on its surroundings? In this theoretical preprint, Tanaya Ray and colleagues investigate that question using a refrigerator made from three qubits: quantum systems with just two energy levels.

One qubit is the cooling target. The other two form the machine, with each qubit connected to its own reservoir. A carefully chosen three-body interaction exchanges an excitation in the target and work qubits for an excitation in the remaining qubit. Matching the associated energies allows this exchange without an external work drive during operation. The reservoirs supply the energy resources that make refrigeration possible.

The researchers ask whether changing the reservoirs’ states, while retaining this basic refrigerator, can lower the target qubit’s temperature.

What makes a reservoir “Kerr-athermal”?

The distinction between preparing a reservoir and operating it is central to the study.

The reservoirs consist of oscillator modes, each capable of holding different numbers of excitations. In an ordinary harmonic thermal reservoir, these occupations follow the equilibrium distribution associated with equally spaced energy levels.

Here, the authors instead specify occupation probabilities using a Kerr-type preparation Hamiltonian: an energy rule with an additional term proportional to the square of the excitation number. This increasingly penalizes highly occupied states, suppressing them relative to the thermal reference.

During refrigerator operation, however, the modes evolve harmonically. Their prepared probabilities remain stationary, but they are not an equilibrium thermal distribution for that operating Hamiltonian. That is what “athermal” means here—not a reservoir with no energy or no temperature-related properties. The preparation-temperature parameter is not its operating equilibrium temperature.

A parameter called zeta controls the modification. Smaller positive zeta means stronger deformation; taking zeta to infinity recovers the ordinary thermal reference.

Following the cooling in time

The team numerically studies an open-system master equation, which describes the refrigerator’s internal evolution together with transitions induced by its surroundings. They use the energy states of the complete interacting refrigerator, rather than treating each qubit’s dissipation independently of the others.

The treatment assumes weak system–reservoir coupling and sufficiently short-lived reservoir memory, alongside a secular approximation that separates different transition frequencies. The qubits start in identical states for the engineered-reservoir and thermal-reservoir comparisons.

The target’s temperature is inferred from its ground-state and excited-state probabilities. A larger ground-state population corresponds to a lower temperature in the situations studied.

The researchers distinguish transient cooling—the early evolution—from the steady state reached after the dynamics settle.

A lasting advantage, not necessarily a deeper early dip

For the parameter sets investigated, the engineered reservoirs lower the target’s steady-state temperature relative to the thermal reference.

In one regime, ordinary thermal reservoirs produce only temporary cooling: the target eventually returns to its initial temperature or above it. Sufficient Kerr-type preparation changes that outcome, leaving the target colder than it began even at steady state.

In another regime, the thermal reference already provides lasting cooling. Reservoir engineering lowers that final temperature further. With sufficiently strong preparation, the steady-state temperature can even fall below the early minimum available with thermal reservoirs.

But the earliest temperature dip is not universally improved. In the examples, it changes little or not at all. For one parameter set, the crossover where the steady state becomes the lowest-temperature point occurs around zeta 50; changing the qubit energies moves it to about 82. These are model-dependent examples, not universal thresholds.

Colder does not mean more efficient

Suppressing reservoir occupations favors qubit relaxation over excitation at the relevant transitions. This helps explain the lower final temperatures, although all three reservoirs and the internal interaction jointly determine the outcome.

The authors also calculate reservoir energy currents and a coefficient of performance: the cold-reservoir energy extraction rate divided by the work-reservoir energy input rate. The steady-state coefficient remains nearly unchanged. The conclusion reports decreased cooling power in the steady-state examples, so the temperature advantage should not be read as faster heat removal.

Crucially, that coefficient excludes the costs of preparing or maintaining the athermal reservoirs.

What remains to be demonstrated

This is an arXiv preprint, revision v2 dated November 9, 2026, reporting theory and numerical calculations—not an experimental refrigerator demonstration.

The paper discusses superconducting resonators and tunable Kerr interactions as possible ingredients, but preparing and maintaining the required reservoir populations remains challenging. The advantage is also not exclusive to Kerr physics: within this model, other suitable reservoirs with matching mean occupations and spectral densities at the relevant frequencies would produce the same dissipative rates. The result identifies reservoir occupation engineering as a route to lower steady-state temperatures, not a demonstrated efficiency breakthrough.