Laser Cooling is Optimized for Efficiency

Rajibul Islam

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Laser Cooling is Optimized for Efficiency

Rajibul Islam

Department of Physics and Astronomy, University of Waterloo, Ontario, Canada

May 21, 2025• Physics 18, 106

A new laser-based cooling scheme approaches the maximum efficiency that is theoretically achievable.

Figure caption — **Figure 1:** Modular-variable cooling uses lasers to squeeze a trapped ion into stillness. (a) An ion in a harmonic trap oscillates with initially zero spin (yellow). (b) The spin-dependent-force (SDF) laser (blue) applies a force to the atom, whose spin precesses more the farther it is from the origin; then, a separate optical laser measures the ion’s spin. (c) The SDF laser pushes the ion (left or right) toward the origin by an amount that corresponds to the measured magnitude of the spin. (d) Finally, the spin is reset to zero, ready for another cooling round (depicted here is the conditional-feedback position; not depicted is conditional feedback along the momentum direction).

Much of the progress in 20th-century physics has centered around understanding the interaction between light and matter. The availability of well-controlled light sources—lasers—enabled experimental exploration of controlled light–matter interactions and, specifically, methods to cool atoms close to absolute zero temperatures [1, 2]. Several laser-cooling methods, such as Doppler cooling and resolved sideband cooling, are used routinely to prepare controlled quantum states of atoms. Brennen de Neeve of the Swiss Federal Institute of Technology (ETH) Zurich and his colleagues now show just how efficient a laser-cooling process can be [3] (Fig. 1). They demonstrate a laser-cooling method that uses a “spin-dependent force” to transfer motional entropy from the atom into the entropy of its internal degrees of freedom. The efficiency of this cooling method, named modular-variable (MV) cooling, is a vast improvement over previous methods for high thermal occupation.

Developed over the past five decades, laser cooling has opened many opportunities. It has made it possible to isolate individual atoms, photograph a gas near absolute zero temperature with atomic resolution [4], and study quantum properties of many-particle systems. The central theme to all laser-cooling methods is the use of an internal state of an atom (its “spin state”) to extract entropy from the motional state of the atom. That motional entropy can be understood by considering the atom confined in a harmonic potential, as occurs with electronic potentials for ions or optical tweezers—tightly focused beams—for neutral atoms. Energy levels of a harmonic oscillator are quantized, and the $n$ th one can be thought of as consisting of $n$ packets of motional energy or phonons. In this picture, the temperature of the atom is given by the average phonon number $\bar{n}$ . At high temperatures, large $\bar{n}$ , the atomic states can be probabilistically distributed over many energy levels: It has a large motional entropy. For cooling purposes, the atom can be initially placed in a well-defined spin state: It has a small (or zero) spin entropy. In each cooling round, motional entropy is transferred to spin entropy by exploiting some aspect of light–matter interactions. The spin entropy is then removed by photon emission, and the spin returns to its well-defined state, ready for the next cooling round.

In their work, De Neeve and his colleagues investigate precisely how much entropy can be removed from an atom in a harmonic potential, which is equivalent to asking how much $\bar{n}$ can be reduced, per cooling round. A maximally efficient cooling scheme would reduce the thermal occupation $\bar{n}$ to $\bar{n} ∕ 2$ (for $\bar{n} ≫ 1$ ), corresponding to the maximum entropy that can be removed by a single spin reset in the cooling round. Yet, all existing cooling techniques are far from this limit. For example, in the commonly used sideband-cooling method, every round lowers $\bar{n}$ to $\bar{n} - 1$ . Thus, for $\bar{n} ≫ 1$ , the cooling efficiency per round is negligible. The trick to increasing the efficiency is to optimally couple spin and motion to maximize entropy transfer.

In their MV-cooling scheme, De Neeve and his colleagues use a versatile tool in trapped-ion physics known as spin-dependent forces (SDF) to couple spin and motion [5]. As the name suggests, an SDF is a force whose direction depends on the spin state. As a simple example, an SDF can be used to push an ion with spin pointing up in one direction, while pushing a spin-down ion in the opposite direction. De Neeve and colleagues’ experiments generate SDFs using laser beams that transfer momentum to a single trapped calcium ion. These lasers have frequencies far detuned from atomic excited states, so they avoid photon scattering and enable coherent motion–spin transitions. Because the time evolution of the ion’s quantum state is reversible under coherent interactions, SDFs cannot directly reduce entropy or cool the system. Rather, they offer a clever way to exchange motional entropy for spin entropy—a crucial step toward cooling.

Of course, an external driving force can change both the position and momentum of a particle confined in a harmonic oscillator. Thus, the action of the SDFs can be understood in terms of the displacements of the ion’s state along both position and momentum directions—the two directions of the so-called phase space. De Neeve and colleagues can precisely control the SDFs by varying the phase and duration of their laser pulses. In the first half of an MV-cooling round, they chose SDFs such that the position spread of the ion (due to its thermal motion) was reduced at the expense of increasing entropy in its spin. They next reset the spin by a standard atomic physics technique—optical pumping—to remove this entropy. In the second half of the cooling round, the team selected SDFs to reduce the spread along the momentum direction, followed by another spin reset. Thus, the ion’s spread in both position and momentum was reduced after a cooling round. This is equivalent to reducing the average phonon number $\bar{n}$ , which leads to cooling.

De Neeve and colleagues offer an intuitive picture to describe their experiment in terms of measurement and conditional feedback. For example, in the first half of a cooling round, the SDFs make the ion spin state tilt more toward “up” the farther right the ion is from the center of the potential. Similarly, the spin is tilted more toward “down” the farther left the ion is. Now imagine that we measure the spin and find it to be “up.” It is then likely that the ion is to the right of the center. Then, a subsequent SDF can be applied to push it toward the center.

De Neeve and colleagues’ experiments lowered the average phonon number $\bar{n}$ to $63$ % of its initial value (for $\bar{n} ≫ 1$ ) after each round of cooling. Although that is far from the theoretical limit of $25$ % of the initial value per round for a maximally efficiency cooling scheme (with the limit coming from two spin resets per round in their scheme), it is nevertheless impressive and significantly more efficient than other methods. Starting with $\bar{n} \approx 50$ , the team’s MV method reached $\bar{n} \approx 0.3$ after about ten cooling rounds, whereas sideband cooling would require about $50$ cycles to achieve comparable results. It’s also worth noting that certain cooling methods are unable to reach these low temperatures. For example, the commonly used Doppler-cooling method, which relies on scattering of many photons, would be limited to $\bar{n} \approx 10$ for the calcium-ion system.

Although their cooling method worked with a high starting $\bar{n} \approx 50$ , there is a limit to how high $\bar{n}$ could be for the cooling method to work. This limit is given by the so-called Lamb-Dicke regime, where the spread of the ion is small compared to the wavelength of the light that creates the SDF. Also, the increased efficiency does not imply that it is the most practical approach. For example, the most common laser-cooling method—Doppler cooling—is extremely inefficient per cooling round, as the displacement in phase space in one cooling round is tiny. Nevertheless, Doppler cooling is much faster, and the starting $\bar{n}$ can be much higher than the MV-cooling method.

However, Doppler cooling is not always applicable, such as in nonatomic systems [6], where the MV cooling can be applied. There are situations where limiting the number of scattered photons would be crucial, such as in cooling molecules [7], where photon-scattering events can “trap” the molecule in undesirable energy levels. In quantum information processing with atom-based qubits, it may be helpful to limit photon scattering that disturbs “data” qubits while cooling the system through “refrigerant” qubits [8]. The MV-cooling method can potentially be a good alternative in these situations, either on its own or combined with another method. The experimental demonstration by De Neeve and colleagues, therefore, not only explores a fundamental physics question about the efficiency of laser-cooling methods but also opens doors to cooling systems that have been out of reach so far.

References

D. J. Wineland et al., “Radiation-pressure cooling of bound resonant absorbers,” Phys. Rev. Lett. 40, 1639 (1978).
W. Neuhauser et al., “Optical-sideband cooling of visible atom cloud confined in parabolic well,” Phys. Rev. Lett. 41, 233 (1978).
B. de Neeve et al., “Modular variable laser cooling for efficient entropy extraction,” Phys. Rev. Lett. 134, 203603 (2025).
W. S. Bakr et al., “A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice,” Nature 462, 74 (2009).
P. C. Haljan et al., “Spin-dependent forces on trapped ions for phase-stable quantum gates and entangled states of spin and motion,” Phys. Rev. Lett. 94, 153602 (2005).
P. Campagne-Ibarcq et al., “Quantum error correction of a qubit encoded in grid states of an oscillator,” Nature 584, 368 (2020).
E. S. Shuman et al., “Laser cooling of a diatomic molecule,” Nature 467, 820 (2010).
J. M. Pino et al., “Demonstration of the trapped-ion quantum CCD computer architecture,” Nature 592, 209 (2021).

About the Author

Rajibul Islam is an associate professor at the University of Waterloo, Canada, where he runs the Laboratory for Quantum Information with Trapped Ions at the Institute for Quantum Computing. His research team is building quantum simulators with laser-cooled trapped ions to simulate models of interacting quantum many-particle systems. Islam is the cofounder of Open Quantum Design, a nonprofit aimed at developing open-source quantum computing, and a fellow of the American Physical Society.