Making a strongly coupled plasma Plasmas—gases of ionized atoms and electrons—are naturally formed at high temperatures, such as those reached in the interiors of stars. Describing plasmas theoretically is tricky when they are in the strongly coupled regime; reaching that regime in the laboratory would provide a valuable benchmark for theory. To that end, Langin et al. worked with a cold plasma created out of atoms of strontium that were ionized by laser light (see the Perspective by Bergeson). They used lasers to cool the ions down to about 50 millikelvin, reaching the desired strongly coupled regime. Science, this issue p. 61; see also p. 33

Abstract Laser cooling of a neutral plasma is a challenging task because of the high temperatures typically associated with the plasma state. By using an ultracold neutral plasma created by photoionization of an ultracold atomic gas, we avoid this obstacle and demonstrate laser cooling of ions in a neutral plasma. After 135 microseconds of cooling, we observed a reduction in ion temperature by up to a factor of four, with the temperature reaching as low as 50(4) millikelvin. This pushes laboratory studies of neutral plasmas deeper into the strongly coupled regime, beyond the limits of validity of current kinetic theories for calculating transport properties. The same optical forces also retard the plasma expansion, opening avenues for neutral-plasma confinement and manipulation.

The application of laser cooling to trapped ions (1–3) and neutral atoms (4) has driven groundbreaking advances in physics, including quantum computing (5), Wigner crystallization (6–8), and quantum degeneracy (9). More recently, laser-cooling techniques have been applied to molecules (10), solids (11, 12), and mesoscopic quantum objects (13). In this study, using an ultracold neutral plasma (UNP) created by photoionizing Sr atoms in an ultracold gas (14, 15), we demonstrate laser cooling of ions in a neutral plasma.

A major motivation for cooling ions in a neutral plasma is to study transport, thermalization, and collective modes when the ratio between the Coulomb potential energy and thermal kinetic energy of ions is large [ , where T i is the ion temperature, a = (3/4πn i )1/3 is the Wigner-Seitz radius for density n i , e is the elementary charge, ε 0 is the vacuum permittivity, and k B is the Boltzmann constant]. Standard kinetic theories (16) fail to describe important plasma properties under such conditions of strong Coulomb coupling because they neglect effects of spatial correlations. Such conditions are found in white dwarf stars (6, 17), cores of Jovian planets (6), dusty plasmas (18), trapped nonneutral plasmas (3, 7, 8), laser-produced plasmas important for studies of warm dense matter and inertial confinement fusion (17, 19), and UNPs. State-of-the-art predictions of transport and thermalization rates for high-density strongly coupled plasmas (20) are currently obtained from direct molecular dynamics simulation (21–23) of the Yukawa one-component-plasma (OCP) model (6, 17, 24). UNPs are highly faithful realizations of the Yukawa OCP model (15). With precise temperature and density diagnostics (14) and pump-probe techniques for studying kinetic processes (25), UNPs offer many advantages for studying the effects of strong coupling on collisional processes (15, 24, 25) and validating numerical methods.

With the use of standard methods for UNP creation, coupling in these systems is limited to by disorder-induced heating (DIH), which occurs immediately after plasma creation from the disordered atomic or molecular gas. DIH decreases the ion Coulomb energy and increases the temperature to T DIH ≈ e2/12πε 0 ak B as ions develop spatial correlations (14, 15, 26). For typical UNP densities, T DIH ~ 1 K. Many schemes have been proposed to overcome this limit, such as precorrelating the system before ionization by using Rydberg blockade (27, 28), Fermi repulsion (26), an optical lattice (28), and molecular Rydberg plasmas in a supersonic beam (29). Sequential excitation to higher ionization states (30) has been shown to increase Γ by 40%. Experiments using Rydberg blockade (31) and molecular plasmas (29) have yielded promising results, but no measured values of Γ have been reported. In this work, we realized laser-cooling proposals (32, 33) and achieved Γ i as high as 11(1).

Laser cooling works through velocity-dependent scattering and exchange of momentum between near-resonant photons and ions, molecules, or atoms. For simple Doppler cooling (4) using a transition with natural linewidth γ (expressed in hertz), excitation wavelength λ, and laser detuning Δ ~ −γ, particles with velocity substantially outside the capture range (v c = λγ) are Doppler-shifted too far out of resonance for appreciable light scattering. Thus, cooling is most effective in systems with for characteristic thermal velocity v T = (k B T/m)1/2, where m is the particle mass. For typical optical transitions, v c ≈ 10 m/s, requiring K. This is one reason that laser cooling has not been successfully applied to ions in non-ultracold neutral plasmas, which are invariably much hotter than UNPs. UNPs provide the required low initial ion temperature, but high collision rates (25) and hydrodynamic expansion of the plasma into surrounding vacuum (14, 15) create an environment that differs markedly from other systems that have been laser cooled.

To create UNPs, we initially cooled 5 × 108 88Sr atoms to T = 1 mK and magnetically trapped them in the metastable 5s5p 3P 2 state by using standard laser-cooling techniques (34). Trapping fields and cooling lasers were then extinguished, and the atom cloud expanded for 6 ms before a pulse (10 mJ for 10 ns) of λ pulse = 322 nm photons from a doubled, pulsed-dye laser ionized 10% of the atoms. The plasma density distribution was well approximated by a slightly asymmetric Gaussian distribution with root mean square (RMS) radii σ x (0) = 2.4(1) mm and σ y / z (0) = 3.1(1) mm and peak density n i (0) = 1.3(3) × 108 cm−3. This yielded a peak T DIH = 0.41(0.03) K. λ pulse was tuned such that ΔE = hc/λ pulse − E PI , the excess photon energy above the photoionization threshold energy E PI , set the electron temperature to T e (0) = 2ΔE/3k B = 15.5(3) K. (Here, h is Planck’s constant, and c is the speed of light.) Electrons were trapped by Coulomb attraction to the ions and formed a neutralizing background with overall nonneutrality on the order of a few percent (14, 15).

Immediately after plasma formation, counterpropagating σ+ and σ− polarized beams near resonance with the 5s 2S 1/2 –5p 2P 3/2 transition at 408 nm (γ = 22.4 MHz) illuminated the plasma, forming a one-dimensional optical molasses (4) for laser cooling along the x direction (Fig. 1). The single-beam peak intensity was I = 100 mW/cm2 (1/e2-intensity radius w = 9 mm, and saturation parameter s 0 = 2.3). Lasers at 1092 and 1033 nm repumped ions from long-lived 2D 3/2 and 2D 5/2 states, returning them to the cooling cycle. Reductions in cooling efficiency caused by coherent coupling of the 2S 1/2 and 2D 5/2 states and resulting electromagnetically induced transparencies (35) were minimized by rapid velocity-changing collisions in the plasma (25). After laser cooling, spatially resolved measurements of ion temperature and density were performed by using laser-induced fluorescence (LIF) on the 2S 1/2 –2P 1/2 transition at 422 nm (36). The LIF laser illuminated a central slice of the plasma (z ≈ 0), providing transverse spatial resolution of 13 μm and resolution along the imaging axis equal to the tight dimension of the LIF light (w z = 2 mm). Unless otherwise specified, temperature was measured along the laser-cooling axis (Fig. 1).

Fig. 1 Principles of laser cooling of a neutral plasma. (A) Sr+-level diagram indicating the wavelengths and decay rates for transitions relevant to cooling and imaging. (B) Experimental schematic. Cooling (408-nm) and repumping (1092- and 1033-nm) lasers were applied in counterpropagating configurations with the indicated polarizations. Light at 422 nm for LIF was shaped by a slit to illuminate a central slice of the plasma. It propagated perpendicular to the imaging axis and, unless otherwise specified, along the laser-cooling axis . Propagation directions for LIF and cooling light are indicated. LIF images were recorded on an intensified charge-coupled device camera. A high-pass dichroic D reflected the cooling laser and transmitted the LIF light. M, mirror; λ/4, quarter-wave plate).

Figure 2, A to C, shows temperature measurements, spatially resolved along the laser-cooling axis, for three different laser-cooling parameters: no cooling light (yellow), detuning from resonance of Δ = −20 MHz [cooling (red)], and Δ = +20 MHz [heating (blue)]. By 5 μs after plasma formation, cooling and heating beams had little effect. Temperature variation across the sample reflected variation in density and the resulting DIH temperature . By 60 μs, the ion temperature was substantially altered by the lasers. In the center of the plasma (x ≈ 0), T i doubled in the heating configuration and was reduced by half for cooling compared with no cooling light. The trend continued for 135 μs of heating or cooling, with the lowest temperature observed, T i = 50(4) mK, providing clear evidence of laser cooling.

Fig. 2 Ion temperature and coupling variation. Shown are the data for laser detuning Δ = −20 MHz [red (cooling)], Δ = 20 MHz [blue (heating)], and no 408-nm laser (yellow). (A to C) Temperature at three different times after plasma creation (as indicated in each panel). Each measurement corresponds to a region with Δx = 260 μm and Δy = 4.5 mm centered at y = 0. Cooling and heating were ineffective at large displacement from the plasma center because the plasma expansion Doppler-shifted these ions out of resonance with the lasers. (D) Temperature versus time in the central region (|x| ≤ 0.5 mm). (E) Coulomb coupling parameter Γ i versus time in the central region. Solid lines in (D) and (E) were calculated by using coupled ion and electron kinetic equations (36). We do not display results from the model for the heating data because the density perturbation was too severe for the model to be applicable (Fig. 3A). Error bars indicate SD.

Cooling was effective only in the central region ( mm), which illustrates the role of plasma expansion. Immediately after plasma formation, the density gradient and electron thermal energy created a radially directed force that drives expansion (14). Although electron-ion thermalization has noticeable effects (37) and the plasma used in this work was slightly asymmetric, an analytic expansion model for a collisionless, spherically symmetric, Gaussian plasma is a satisfactory approximation for developing an intuitive explanation of laser-cooling results. In this model (14, 15), expansion creates a hydrodynamic plasma-velocity field (where r is the displacement from the plasma center, t is time, and τ exp = [m i σ(0)2/k B T e (0)]1/2 is a characteristic time for the expansion). The velocity increases with time and distance from the plasma center, saturating at an RMS value for the entire plasma of on a time scale of τ exp . Cooling is effective only in regions for which the expansion velocity along the cooling-laser axis remains less than or comparable to the velocity capture range for an appreciable time.

For these experiments, σ(0)/τ exp ≈ 40 m/s exceeded the velocity capture range, and τ exp ≈ 75 μs was on the order of the minimum time required to scatter enough photons to substantially cool the ions (4). Thus, cooling was most effective for mm, where the expansion velocity stayed relatively small. Analogous statements can be made for the heating configuration. To observe substantial laser cooling, it was essential to create very large plasmas compared with those in previous UNP experiments (14, 15), which increased τ exp and gave more time for laser cooling.

Figure 2D shows the evolution of the ion temperature for the center of the plasma, where cooling and heating were most effective. Fits from an approximate kinetic model (14, 37) accounting for DIH, electron-ion heating, adiabatic cooling, and laser cooling describe the data reasonably well (36). The natural dynamics, seen in the data for no laser cooling, was an increase to T i ~ 0.4 K within the first few microseconds, owing to DIH, followed by cooling caused by adiabatic expansion. In the presence of the cooling lasers, however, the ion temperature dropped much farther than that for no 408-nm light. Even more notable is the increase of Γ i to 11(1) after 135 μs (Fig. 2E), which is comparable to conditions of interest in white dwarf stars (6, 17), for example. It is also much deeper into the strong coupling regime than has previously been reported with these systems. A value of Γ i = 4 was obtained (38) in a UNP with relatively high density and low electron temperature, which induces substantial screening of ion-ion interactions [screening parameter κ = a/λ D = 1 for Debye screening length λ D = (k B T e ε 0 /n e e2)1/2] and reduces the effects of strong coupling. For our conditions, κ ≤ 0.7, and the screening was weaker.

Although laser-cooling was applied only along one axis, all three degrees of freedom were effectively cooled because of the high collision rate in the plasma. Molecular dynamics simulations (39) show that local thermal equilibrium is established on the time scale of a few times the inverse of the ion plasma oscillation frequency, . We confirmed cross-thermalization by measuring the temperature transverse to the cooling axis (36). Lasers along a single axis also produce three-dimensional cooling in trapped ions (1, 2), but this is not true for neutral atoms (4) and molecules (10), which have much lower collision rates. Collisions did not damp the hydrodynamic expansion velocity transverse to the laser-cooling axis because of conservation of momentum during each collision.

The light-scattering force from the cooling lasers also notably retarded the expansion of the plasma, as shown in Fig. 3 for the same initial plasma conditions as in Fig. 2. The kinetic model discussed above provides a reasonable description of the evolution of the RMS size along the laser axis (Fig. 3B). For larger initial plasma size and detuning of the cooling laser, retardation of the expansion was even more effective (36), raising the intriguing possibility of confining a neutral plasma with optical forces, perhaps with the addition of spatially varying magnetic fields in a hybrid magneto-optical trap (4) and magnetic cusp (40) configuration. For blue detuning, the plasma bifurcated because ions were accelerated away from the center until the force diminished when the velocity exceeded the capture range. The marked change in expansion dynamics for blue detuning highlights the potential of laser forces for manipulating a plasma.

Fig. 3 Influence of laser forces on plasma expansion. (A) Evolution of plasma density distribution. Red-detuned optical molasses along retarded expansion, whereas blue-detuned light accelerated it, eventually leading to bifurcation. The scale bar is 5 mm. The color bar is rescaled for each time to n max = (13, 8.5, 4.2, 2.2, 1.3) × 107 cm−3 for t = (5, 30, 60, 90, 120) μs. (B) RMS radius σ x (t) from Gaussian fit to experimental data (same symbols as in Fig. 2). Error bars indicate SD.

Figure 4 illustrates the variation of laser-cooling and heating effects with detuning Δ. After 135 μs of laser application, Γ i in the central region was minimized for Δ ~ −20 MHz. However, as the lasers were further red detuned, more of the cloud experienced the light-scattering forces for a longer time, creating a larger region of cooled ions at the expense of slightly decreased cooling efficiency (Fig. 4A, inset). Similarly, the acceleration of plasma expansion for the heating configuration was most effective for a relatively large blue detuning, Δ ~ 50 MHz, as shown in the plot of RMS size along the laser axis (Fig. 4B).

Fig. 4 Effects of detuning. (A) Temperature at x = 0 versus detuning for 135 μs of evolution in the optical field. The inset shows T i versus x for Δ = −10 MHz (red) and Δ = −30 MHz (blue), along with Gaussian fits. (B) Plasma size versus detuning at 135 μs of evolution. Here, size is the RMS width calculated numerically from the image. Error bars indicate SD.

With Γ i = 11, laser-cooled UNPs are already in an interesting regime for applying established techniques for measuring collision rates, transport, and dispersion relations (15, 25). Laser forces also open entirely new possibilities. For example, by patterning the lasers spatially, it should be possible to create reasonably sharp velocity gradients and measure shear viscosity. Heating and cooling separate regions of the plasmas should initiate heat flow and allow measurement of thermal conductivity. There are also straightforward opportunities to improve the laser-cooling process, such as investigating cooling along three dimensions, which might be effective for plasma confinement. Increasing the number of ionized atoms would allow for larger σ 0 and τ exp for a given density. Laser cooling could then be applied for a longer time, leading to lower temperature and higher Γ i . The lowest temperature theoretically achievable with Doppler cooling on this transition is T Doppler = hγ/2k B = 0.5 mK (4), and even with present conditions it is likely that cooling can continue longer than reported here and below 50 mK. However, the natural linewidth of the LIF transition is already large compared with the Doppler broadening at this temperature, limiting further application of this temperature diagnostic. Improving the temperature resolution by, for example, using a narrow two-photon transition to a metastable D state should enable measurement of lower temperature. Then it will be possible to study the laser-cooling and laser-confinement limits imposed by electron-ion heating and three-body recombination (14, 15, 32).

Supplementary Materials www.sciencemag.org/content/363/6422/61/suppl/DC1 Supplementary Text Figs. S1 to S4 References (42–49)

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