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Physica Scripta

Quantum droplets and Schrödinger cat-like states in atomic-molecular Bose-Einstein condensates

Leena Barshilia, Rajiuddin Sk, Prasanta Kumar Panigrahi, Avinash Khare

Published May 28, 2025• 0 citations
Publisher

Abstract

Abstract Explicit realization of quantum droplets, even and odd Schrödinger cat-like states is demonstrated in an atom-molecular Bose-Einstein condensate in the presence of interconversion and Kerr non-linear interactions. The crucial roles of both the χ2-type nonlinearity and chemical potential in the formation of these macroscopic quantum states are shown, where the atomic condensate is in the cat-like state, with the corresponding molecular wave packet being a quantum droplet. The physical mechanism for their creation and common origin is established to be the non-linearity-induced self-trapping potentials, governed by photoassociation or Feshbach resonance, with the Kerr-type nonlinearities playing subdominant roles. The coexisting and controllable atom and molecular droplets are shown to realize the atom-molecular squeezed state with profiles ranging from Gaussian to flat-top super-Gaussian form. The Wigner functions are exhibited revealing the cat-like states' phase space interference and squeezing of droplets.

DOI
10.1088/1402-4896/adddf5

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Abstract Explicit realization of quantum droplets, even and odd Schrödinger cat-like states is demonstrated in an atom-molecular Bose-Einstein condensate in the presence of interconversion and Kerr non-linear interactions. The crucial roles of both the χ2-type nonlinearity and chemical potential in the formation of these macroscopic quantum states are shown, where the atomic condensate is in the cat-like state, with the corresponding molecular wave packet being a quantum droplet. The physical mechanism for their creation and common origin is established to be the non-linearity-induced self-trapping potentials, governed by photoassociation or Feshbach resonance, with the Kerr-type nonlinearities playing subdominant roles. The coexisting and controllable atom and molecular droplets are shown to realize the atom-molecular squeezed state with profiles ranging from Gaussian to flat-top super-Gaussian form. The Wigner functions are exhibited revealing the cat-like states' phase space interference and squeezing of droplets.
Explicit realization of quantum droplets, even and odd Schrödinger cat states is demonstrated in an atom-molecular Bose-Einstein condensate in the presence of interconversion and Kerr non-linear interactions. The crucial roles of both the χ2χ^2χ2-type nonlinearity and chemical potential in the formation of these macroscopic quantum states are shown, where the atomic condensate is in the cat state, with the corresponding molecular wave packet being a quantum droplet. The physical mechanism for their creation and common origin is established to be the non-linearity-induced self-trapping potentials, governed by photoassociation or Feshbach resonance, with the Kerr-type nonlinearities playing subdominant roles. The coexisting and controllable atom and molecular droplets are shown to realize the atom-molecular squeezed state with profiles ranging from Gaussian to flat-top super-Gaussian form. The Wigner functions are exhibited revealing the cat states' phase space interference and squeezing of droplets.
Recently, neutral atoms have emerged as a promising platform for quantum computing, offering scalability. In this study, we showcase the realization of atomic qubits in atom-molecular Bose-Einstein condensate, belonging to three distinct classes. In the first case, the condensed molecules form a droplet platform with a flat-top configuration, facilitating effective isolation from both external environments and neighbouring molecules. The second atomic qubits have wavefunctions in the ``pulse" form, exhibiting power law behaviour, whereas the third one has ground and excited state wavefunctions in their respective composite forms, $\sech^2{βx}$ and $\sech{βx}\tanh{βx}$. The localization of the qubits depends on the chemical potential, which is governed by the photo association, providing effective control for qubit manipulation. The relevant parameters, such as energy level separation, healing length, and atom numbers, are found to be influenced by the non-linearity and strength of photo associations governing the behaviour of macroscopic qubits and molecular droplets.
Quantum droplets have recently emerged as a novel liquid state of matter in a mixture of two-component ultracold Bose gases under the equilibrium condition between the competing attractive inter- and repulsive intraspecies forces. Quantum droplets represent a self-bound liquid state in purely nonlinear systems and as such there is not any management applied to their study up to now. We here introduce the nonlinear management via space-periodic Feshbach resonance technique to a binary Bose–Einstein condensate and investigate theoretically the structure, property and dynamics of the one-dimensional quantum droplets therein, three findings are made: small droplets with single hump (solitonlike), moderate droplets composed of two solitons, large droplets feature a modulated flat-top shape. Particularly, by means of linear-stability and direct perturbed simulations, we prove that the droplets have a much wider stable region than their counterparts without taking the nonlinear management. The variational approximation is adopted and validated with numerical results in terms of small droplets. The results predicted here may be realized in the frontier ultracold atoms experiments aided by Feshbach-resonance, opening up a new channel to the quantum droplets studies.
Quantum droplets represent a novel state of matter achieved by tailoring a binary Bose–Einstein condensate, where the collapse driven by self-attraction is arrested by quantum effects. This opens the possibility of producing interesting novel physical phenomena, which require accurate mathematical models for its correct description. In this work, we apply variational procedures to the mean field equation governing two-dimensional symmetric quantum droplets, to find simple yet very precise formulae for the droplet profile and the relationships between its main parameters, such as internal and external radii of the bright rings, the chemical potential or the number of atoms of the droplets. The comparison with direct numerical calculations demonstrates that our model provides a highly accurate description of the self-trapped eigenstates with flat-top profiles. These results should aid in the exploration of additional effects in liquid-like solitons and vortex states endowed with angular momentum.
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We propose and numerically validate a scheme for the realization of Schrödinger cat-like states in a two-component Bose-Einstein condensate, emphasizing their twinning across components under tunable intra- and inter-species interactions within the miscibility regime. Wigner phase-space analysis reveals sub-Planck-scale interference fringes, confirming the nonclassical character of the states and their potential utility in quantum-enhanced metrology. The dynamical response of the system to a weak linear gravitational-like perturbation further demonstrates cooperative enhancement: while the directly perturbed component retains its cat-like features, the coupled partner exhibits a pronounced population imbalance and a distinct phase-space rotation, providing a sensitive detection channel absent in single-component condensates. These results establish binary condensates as a versatile platform for engineering macroscopic quantum superpositions and exploiting their twinning dynamics for precision measurements.