Ultracold Atoms Reveal a New Type of Transition for Precise State Control

Scientists have demonstrated a first-order phase transition within a quantum degenerate mixture of atoms and molecules, revealing a novel pathway for controlling ultracold reaction dynamics. G. A. Bougas, A. Vardi, and H. R. Sadeghpour from the Institute for Research in Electronics and Applied Physics at the University of Maryland, alongside C. Chin working with colleagues at the University of Chicago and S. I. Mistakidis, mapped the phase diagram of a two-mode atom-molecule Bose-Einstein condensate incorporating Fano-Feshbach resonance and coherent three-body recombination. Their research establishes that, unlike typical second-order transitions, prominent coherent three-body recombination induces a double-well structure in the free energy landscape, leading to atom-molecule entanglement, bistability, and molecular metastability. This discovery provides a powerful mechanism for state engineering and precise control over reaction processes in ultracold atomic systems.

This work details how coherent three-body recombination (cTBR) fundamentally alters the behaviour of these condensates, shifting a standard, gradual change into an abrupt, first-order phase transition. Traditionally, tuning the energy of molecules within these condensates induces a smooth shift between atomic and molecular states. However, when cTBR, a reversible process converting atoms into molecules and vice versa, becomes dominant, the system undergoes a dramatic, discontinuous change in its composition. This transition is not merely a shift in the balance between atoms and molecules, but is intimately linked to quantum entanglement, a key resource for quantum technologies. The research demonstrates that the system can exist in multiple stable states simultaneously, a property known as bistability, and exhibits a tendency towards a unique atom-molecule “cat state”, a superposition of atomic and molecular configurations. These findings establish cTBR as a powerful tool for engineering quantum states and manipulating reaction dynamics at extremely low temperatures. The study focuses on two-mode condensates, systems where atoms and molecules occupy distinct quantum states, and meticulously maps the conditions under which this novel phase transition occurs. By carefully balancing the Feshbach coupling, the standard method for creating these molecules, with cTBR, scientists have identified a regime where the free energy landscape develops a double-well structure. This double-well is the origin of the first-order transition and the associated bistability, offering unprecedented control over the condensate’s quantum properties. The implications extend to precision measurements, quantum simulation, and even the development of new quantum chemical processes. Initial analysis of the two-mode atom-molecule Bose-Einstein condensate reveals a striking first-order phase transition when cTBR dominates over direct Feshbach coupling. This transition manifests as a discontinuous drop in molecular ground state occupation as the atom-molecule detuning is varied, a departure from the expected second-order transition observed with purely Feshbach-driven processes. The research establishes a clear link between cTBR strength and the emergence of this novel phase behaviour, identifying a double-well structure within the mean-field free energy landscape of the atom-molecule system, directly responsible for the first-order transition. This double-well configuration features distinct minima corresponding to a purely molecular condensate and a coherent superposition predominantly composed of atoms. The dimensionless parameters governing this behaviour are δ, representing the detuning in units of the Fano-Feshbach resonance width, and γ, quantifying the ratio of cTBR strength to Feshbach coupling, both serving as key control parameters. In the vicinity of the transition, the system exhibits bistability, resulting in a nonclassical ground state characterised by substantial atom-molecule entanglement. This entanglement tends towards an atom-molecule cat state, a superposition of molecular and atomic components. Quench protocols were proposed to demonstrate the metastability of the molecular condensate beyond the phase transition, contrasting with the instability seen under purely Feshbach coupling. The observed metastability is also dependent on the total atom number, N. The model employed considers NA atoms and NM molecules, with fractional populations defined by fA = NA/N and fM = NM/N, subject to the constraint 1 = fA + 2fM. The two-mode Hamiltonian incorporates the detuning ∆, the Feshbach coupling g2, and the cTBR strength g3, all within a volume V and density n = N/.

A two-mode Hamiltonian underpins the investigation of atom-molecule Bose-Einstein condensates, meticulously designed to capture the interplay between Feshbach coupling and cTBR. This Hamiltonian, expressed in terms of bosonic annihilation operators for atoms and molecules, describes a system comprising NA atoms and NM molecules confined within a volume V, with a total particle number N. The model incorporates a detuning parameter, ∆, which is experimentally controlled via external magnetic fields and governs the energy of the Feshbach molecule. Feshbach coupling, represented by the term g2, facilitates the reversible conversion between two atoms and a single molecule, while the cTBR term, g3, accounts for the reversible collision of three atoms to form a molecule and a free atom. To explore the phase diagram, the research focused on the ground state properties of this atom-molecule condensate, deliberately choosing this approach to reveal the fundamental mechanisms driving the observed transitions. This contrasts with time-dependent analyses, allowing for a precise determination of the equilibrium states under varying conditions. The chosen Hamiltonian prioritises clarity and computational efficiency, enabling a detailed mapping of the free energy landscape and identification of potential instabilities. Specifically, the study examines the competition between the Feshbach coupling and cTBR, investigating how their relative strengths influence the system’s behaviour. The model’s simplicity, focusing on only two modes (atom and molecule), allows for a robust analytical and numerical treatment of the many-body interactions, capturing the essential physics of the phase transition within this minimal framework. Scientists have long sought to exert precise control over matter at the quantum level, and this work represents a subtle but significant advance in that endeavour. The ability to engineer phase transitions is crucial for building advanced technologies, but achieving this control in complex systems like Bose-Einstein condensates has proven remarkably difficult. The challenge lies in balancing competing forces and understanding how interactions between particles shape the overall behaviour. This research demonstrates a novel method for manipulating these interactions, specifically through cTBR, to induce a first-order phase transition where previously only a second-order transition existed. What makes this particularly notable is the demonstration of bistability and molecular metastability, hinting at a richer landscape of potential states than previously anticipated. The system doesn’t simply move from one state to another; it can exist in multiple stable configurations simultaneously, opening doors to more complex quantum operations. The observed entanglement between atoms and molecules, while not maximal, is a key resource for quantum technologies, and the ability to enhance this entanglement near phase transitions is a valuable tool. However, scaling up these systems remains a considerable hurdle. The narrowing of avoided crossings at higher atom numbers suggests that the enhanced tunneling, and therefore the control offered by this method, may be limited by system size. Future work will likely focus on mitigating these limitations, perhaps through alternative geometries or stronger interactions. Beyond this specific system, the principles demonstrated here could be applied to other ultracold atom platforms and, speculatively, to the design of novel materials with tailored quantum properties.