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arXiv:2601.18839 · Physical Review A

Quantum Simulation of the Polaron-Molecule Transition on a NISQ Device

Hugo Catala, Ezequiel Valero, German Rodrigo

quant-phSubmitted Jan 26, 2026• Announced Jan 27, 2026• 0 citations• Revised Feb 16, 2026 (v2)
v1 · Jan 26, 2026v2 · Feb 16, 2026v3 · Jul 10, 2026
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Abstract

The simulation of strongly correlated fermionic systems remains one of the most significant challenges in computational physics due to the exponential growth of the Hilbert space and the fermionic sign problem. In this work, we present a digital quantum simulation framework to explore the Fermi polaron and the Bose-Einstein Condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) crossover. We develop a unified Hamiltonian formalism that bridges pairing superfluidity and impurity physics, mapping the system onto a gate-based quantum processor via the Jordan-Wigner transformation. Using a first-order Trotter-Suzuki decomposition, we implement a Ramsey interferometry protocol to extract the real-time dynamics and spectral response of the system. Our results demonstrate a smooth transition from a dressed quasiparticle (polaron) regime to a stable molecular bound state, characterized by a linear energy renormalization in the strong-coupling limit. We validate our simulation against exact classical benchmarks and report successful execution on the Barcelona Supercomputing Center quantum hardware. Despite the inherent noise of the quantum hardware, the hybrid variational approach shows remarkable resilience, accurately capturing the bifurcation of the spectral density

Journal reference
Phys. Rev. A (2026)
DOI
10.1103/2kdj-6pdz
Comments
11 pages, 9 figures

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The simulation of strongly correlated fermionic systems remains one of the most significant challenges in computational physics due to the exponential growth of the Hilbert space and the fermionic sign problem. In this work, we present a digital quantum simulation framework to explore the Fermi polaron and the Bose-Einstein Condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) crossover. We develop a unified Hamiltonian formalism that bridges pairing superfluidity and impurity physics, mapping the system onto a gate-based quantum processor via the Jordan-Wigner transformation. Using a first-order Trotter-Suzuki decomposition, we implement a Ramsey interferometry protocol to extract the real-time dynamics and spectral response of the system.
Our results demonstrate a smooth transition from a dressed quasiparticle (polaron) regime to a stable molecular bound state, characterized by a linear energy renormalization in the strong-coupling limit. We validate our simulation against exact classical benchmarks and report successful execution on the Barcelona Supercomputing Center quantum hardware. Despite the inherent noise of the quantum hardware, the hybrid variational approach shows remarkable resilience, accurately capturing the bifurcation of the spectral density
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We investigate the system of a heavy impurity embedded in a paired two-component Fermi gas at the crossover from a Bose-Einstein condensate (BEC) to a Bardeen-Cooper-Schrieffer (BCS) superfluid via an extension of the functional determinant approach (FDA). FDA is an exact numerical approach applied to study manifestations of Anderson's orthogonality catastrophe (OC) in the system of a static impurity immersed in an ideal Fermi gas. Here, we extend the FDA to a strongly correlated superfluid background described by a BCS mean-field wave function. In contrast to the ideal Fermi gas case, the pairing gap in the BCS superfluid prevents the OC and leads to genuine polaron signals in the spectrum. Thus our exactly solvable model can provide a deeper understanding of polaron physics. In addition, we find that the polaron spectrum can be used to measure the superfluid pairing gap, and in the case of a magnetic impurity, the energy of the subgap Yu-Shiba-Rusinov (YSR) bound state. Our theoretical predictions can be examined with state-of-art cold-atom experiments.
We investigate the zero-temperature quasiparticle properties of a mobile impurity immersed in a strongly interacting Fermi superfluid at the crossover from a Bose-Einstein condensate (BEC) to a Bardeen-Cooper-Schrieffer (BCS) superfluid, by using a many-body TTT-matrix approach that excludes Efimov trimer bound states. Termed the BEC-BCS crossover polaron, or crossover polaron in short, this quasiparticle couples to elementary excitations of a many-body background and therefore could provide a useful probe of the underlying strongly interacting Fermi superfluid. Due to the existence of a significant pairing gap $\mathrm{\ensuremath{\Delta}}$, we find that the repulsive polaron branch becomes less well defined. In contrast, the attractive polaron branch is protected by the pairing gap and becomes more robust at finite momentum. It remains as a delta-function peak in the impurity spectral function below a threshold $2\mathrm{\ensuremath{\Delta}}$. Above the threshold, the attractive polaron enters the particle-hole continuum and starts to get damped. We predict the polaron energy, residue, and effective mass for realistic Bose-Fermi mixtures, where the minority bosonic atoms play the role of impurity. These results are practically useful for future cold-atom experiments on crossover polarons.
Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.
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Confined ultracold atoms in optical lattices provide a versatile platform for simulating lattice models of strongly correlated quantum systems, where pairing phenomena and superfluid phases can be explored under controlled conditions. While the crossover between the Bardeen-Cooper-Schrieffer (BCS) phase and the Bose-Einstein condensation (BEC) is well understood in homogeneous systems, spatial confinement breaks translational symmetry and reshapes correlation patterns, making the BCS-BEC identification in trapped geometries challenging and allowing unconventional phases to emerge with no direct analog in homogeneous systems. Here we present a characterization of the BCS-BEC crossover in harmonically confined one-dimensional Fermi-Hubbard chains. Our analysis combines Density Matrix Renormalization Group (DMRG) simulations and entanglement-based diagnostics with effective models describing the formation of tightly bound fermion pairs. This combined approach enables a detailed understanding of how the interplay between interactions and confinement reshapes the crossover, leading to insulating regions coexisting with persistent superfluid correlations. Within this framework, we further introduce conditioned correlation functions whose power-law decay allows a clear distinction between BCS-like and BEC-like regimes. The consistency between the effective descriptions and the numerical DMRG results yields a unified picture of the crossover in harmonically confined geometries.