Dipolar quantum gases: from 3D to Low dimensions

Dipolar quantum gases, encompassing atoms and molecules with significant dipole moments, exhibit unique long-range and anisotropic dipole-dipole interactions (DDI), distinguishing them from systems dominated by short-range contact interactions. This review explores their behavior across dimensions, focusing on magnetic atoms in quasi-2D in comparison to 3D. In 3D, strong DDI leads to phenomena like anisotropic superfluidity, quantum droplets stabilized by Lee-Huang-Yang corrections, and supersolid states with density modulations. In 2D, we discuss a new scenario where DDI induces angle-dependent Berezinskii-Kosterlitz-Thouless transitions and potential supersolidity, as suggested by recent experimental realizations of strongly dipolar systems in quasi-2D geometries. We identify key challenges for future experimental and theoretical work on strongly dipolar 2D systems. The review concludes by highlighting how these unique 2D dipolar systems could advance fundamental research as well as simulate novel physical phenomena.

💡 Research Summary

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This review article provides a comprehensive overview of dipolar quantum gases—both magnetic atoms and electric‑dipole molecules—focusing on how their long‑range, anisotropic dipole‑dipole interactions (DDI) manifest in three‑dimensional (3D) traps and in quasi‑two‑dimensional (quasi‑2D) geometries. The authors begin by cataloguing the principal dipolar species: chromium (6 μB), dysprosium (10 μB), erbium (7 μB), and recently realized europium, as well as polar molecules such as KRb and NaRb whose electric dipole moments can be tuned by external fields. They emphasize that the dipolar length (a_{dd}) for lanthanide atoms is substantially larger than for alkali atoms because of their heavier mass, making them ideal platforms for exploring strong‑dipole physics.

The two‑body interaction is expressed as a sum of a contact pseudopotential and the DDI term (V(\mathbf r)=g_{3D}\delta(\mathbf r)+g_{3D}^{dd}(1-3\cos^2\alpha)/r^3). While this decomposition is rigorously valid only for weak dipoles far from scattering resonances, it serves as a useful starting point. In the strong‑dipole regime the relative dipolar strength (\epsilon_{dd}=a_{dd}/a_s) can exceed unity, and temperature‑dependent corrections to (a_{dd}) become important.

In 3D, the interplay between DDI and trap geometry leads to a rich set of phenomena. In cigar‑shaped traps where dipoles align along the long axis, the attractive component of DDI drives a mean‑field collapse once the s‑wave scattering length (a_s) falls below a critical value; the ensuing “cloverleaf” pattern observed after time‑of‑flight expansion is a hallmark of the dipolar collapse. Conversely, in pancake‑shaped traps the dipoles repel each other along the tightly confined direction, stabilizing the gas even for negative (a_s). When the net mean‑field interaction (contact plus DDI) nearly vanishes, beyond‑mean‑field quantum fluctuations—captured by the Lee‑Huang‑Yang (LHY) correction—stabilize self‑bound quantum droplets. Experiments with Dy and Er have demonstrated both isolated droplets and ordered droplet arrays, with the droplet density sharply increasing at the BEC‑droplet transition.

Collective excitations are strongly anisotropic. The Fourier transform of the DDI yields a momentum‑space potential (V(k)=4\pi\hbar^2 a_s/m + a_{dd}(3\cos^2\theta_k-1)), leading to direction‑dependent excitation spectra. Bragg spectroscopy and measurements of the critical superfluid velocity confirm that the superfluid response is faster along the dipole direction than perpendicular to it. Introducing anisotropic confinement along the dipole axis produces a roton‑like minimum in the dispersion. The roton wavevector scales as (k_{\rm rot}\propto 1/l_z) (with (l_z) the harmonic oscillator length of the tight axis). By increasing (\epsilon_{dd}) or the density, the roton gap can be driven to zero, triggering a roton instability. This instability populates the roton mode, generating density modulations with period (2\pi/k_{\rm rot}) on top of the superfluid background. The resulting state simultaneously breaks the continuous (U(1)) phase symmetry and translational symmetry, realizing a supersolid. The LHY term again prevents runaway density growth, allowing a stable supersolid lattice of droplets immersed in a coherent BEC. Experiments have observed one‑dimensional stripe supersolids, as well as more complex zig‑zag and hexagonal arrangements when the trap geometry is varied.

Turning to two dimensions, the authors first discuss the idealized pure‑2D case where dipoles are confined to the (xy) plane and polarized at an angle (\theta) relative to the (z) axis. The interaction becomes (V(r)=C_{dd}(1-3\sin^2\theta\cos^2\phi)/r^3). A critical angle (\theta_c\simeq35.3^\circ) separates a regime of purely repulsive interactions from one where head‑to‑head configurations become attractive, potentially leading to bound states and collapse. In the weak‑dipole limit the scattering can be described by an effective 2D s‑wave length (a_s) that depends on (\theta), and a hard‑disk model captures the universal low‑density equation of state.

In realistic quasi‑2D traps (tight harmonic confinement along (z)), the DDI is partially “shielded,” reducing inelastic dipolar relaxation. This enables the observation of stable 2D dipolar gases of fermionic molecules and of bosonic Er/Dy atoms with controllable dipole orientation. A major breakthrough has been the observation of a Berezinskii‑Kosterlitz‑Thouless (BKT) transition whose critical temperature varies with the polarization angle, confirming theoretical predictions of anisotropic vortex‑antivortex binding in dipolar superfluids. Monte‑Carlo simulations predict, and recent experiments verify, that sufficiently strong DDI can drive the system into a 2D supersolid phase characterized by simultaneous phase coherence and a periodic density modulation within the plane.

The review concludes by outlining key challenges for 2D dipolar systems: (i) achieving sub‑degree control of the dipole angle and of the confinement frequency to fine‑tune the effective interaction; (ii) suppressing residual losses via electric‑field or microwave shielding; (iii) developing theoretical frameworks that incorporate higher‑order quantum fluctuations beyond the LHY term, especially at finite temperature; and (iv) scaling up system sizes to reach the thermodynamic limit where true phase transitions can be observed. Overcoming these hurdles would position strongly dipolar 2D gases as versatile quantum simulators for exotic phases such as anisotropic superfluids, topological defects, and lattice‑free supersolids, thereby deepening our understanding of long‑range interacting quantum matter.