Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2307.16269 · Physical Review A

Finite-temperature quantum matter with Rydberg or molecule synthetic dimensions

Sohail Dasgupta, Chunhan Feng, Bryce Gadway, Richard T. Scalettar, Kaden R. A. Hazzard

Published Jun 17, 2024• 4 citations
arXivHTMLPDF

Abstract

Synthetic-dimension platforms offer unique pathways for engineering quantum matter. We compute the phase diagram of a many-body system of ultracold atoms (or polar molecules) with a set of Rydberg states (or rotational states) as a synthetic dimension, where the particles are arranged in real space in optical microtrap arrays and interact via dipole-dipole exchange interaction. Using mean-field theory, we find three ordered phases---two are localized in the synthetic dimension, predicted as zero-temperature ground states by Sundar et al. [Sci. Rep. 8, 3422 (2018); Phys. Rev. A 99, 013624 (2019)], and one is a delocalized phase. We characterize them by identifying the spontaneously broken discrete symmetries of the Hamiltonian. We also compute the phase diagram as a function of temperature and interaction strength for both signs of the interaction. For system sizes with more than six synthetic sites and attractive interactions, we find that the thermal phase transitions can be first or second order, which leads to a tricritical point on the phase boundary. By examining the dependence of the tricritical point and other special points of the phase boundary on the synthetic dimension size, we shed light on the physics for thermodynamically large synthetic dimension.

DOI
10.1103/physreva.109.063322

Related papers

Quantum membrane phases in synthetic lattices of cold molecules or Rydberg atoms

Chunhan Feng, Hannah J. Manetsch, V. G. Rousseau +2 more

We calculate properties of dipolar interacting ultracold molecules or Rydberg atoms in a semisynthetic three-dimensional configuration---one synthetic dimension plus a two-dimensional real-space optical lattice or periodic microtrap array---using the stochastic Green's function quantum Monte Carlo method. Through a calculation of thermodynamic quantities and appropriate correlation functions, along with their finite-size scalings, we show that there is a second-order transition to a low-temperature phase in which two-dimensional ``sheets'' form in the synthetic dimension of internal rotational or electronic states of the molecules or Rydberg atoms, respectively. Simulations for different values of the interaction $V$, which acts between atoms or molecules that are adjacent both in real and synthetic space, allow us to compute a phase diagram. We find a finite-temperature transition at sufficiently large $V$ as well as a quantum phase transition---a critical value ${V}_{c}$ below which the transition temperature vanishes.

arXiv:2202.08540•Physical Review A•Jun 21, 2022•13 citations

Synthetic dimensions in ultracold polar molecules

Bhuvanesh Sundar, Bryce Gadway, Kaden R. A. Hazzard

Synthetic dimensions alter one of the most fundamental properties in nature, the dimension of space. They allow, for example, a real three-dimensional system to act as effectively four-dimensional. Driven by such possibilities, synthetic dimensions have been engineered in ongoing experiments with ultracold matter. We show that rotational states of ultracold molecules can be used as synthetic dimensions extending to many - potentially hundreds of - synthetic lattice sites. Microwaves coupling rotational states drive fully controllable synthetic inter-site tunnelings, enabling, for example, topological band structures. Interactions leads to even richer behavior: when molecules are frozen in a real space lattice with uniform synthetic tunnelings, dipole interactions cause the molecules to aggregate to a narrow strip in the synthetic direction beyond a critical interaction strength, resulting in a quantum string or a membrane, with an emergent condensate that lives on this string or membrane. All these phases can be detected using local measurements of rotational state populations.

arXiv:1708.02112•Scientific Reports•Feb 15, 2018•74 citations

Classical Analog of Quantum Models in Synthetic Dimensions

Cohen, Max, Max Casebolt, Yutan Zhang +2 more

We introduce a classical analog of quantum matter in ultracold molecule -- or Rydberg atom -- synthetic dimensions, extending the Potts model to include interactions J1 between atoms adjacent in both real and synthetic space and studying its finite temperature properties. For intermediate values of J1, the resulting phases and phase diagrams are similar to those of the clock and Villain models, in which three phases emerge. There exists a sheet phase analogous to that found in quantum synthetic dimension models between the high temperature disordered phase and the low temperature ferromagnetic phase. We also employ machine learning to uncover non-trivial features of the phase diagram using the learning by confusion approach. The key result there is that the method is able to discern several successive phase transitions.

arXiv:2212.07017•Dec 14, 2022•2 citations

Collective quantum phenomena in strongly correlated multi-level systems

Sohail Dasgupta

In this dissertation, I theoretically investigate the equilibrium properties of three strongly correlated multi-level quantum platforms -- synthetic dimension using ultracold Rydberg atoms, multi-flavor Fermi-Hubbard simulators with ultracold atoms, and magnon-spin coupled rare-earth orthoferrites -- using various numerical and analytical methods. After the broad research motivation in the first chapter, Chapter 2 introduces the general principles of quantum simulation using synthetic dimension platforms. Chapter 3 discusses the first realization with Rydberg atom platform to simulate the topological Su-Schrieffer-Heeger (SSH) model, and how environmental noise affects it. Chapter 4 shows the mean-field phase diagram of dipole-coupled ultracold Rydberg atom arrays exhibiting quantum strings and other ordered states. The connection of the thermal phase transition to that of a classical extended Potts model is also discussed from a renormalization (RG) and generalized duality perspective. These examples illustrate the versatility of synthetic dimension in simulating and engineering quantum phenomena. Chapters 5-6 explore the properties of multi-flavor Fermi-Hubbard models on square optical lattices using numerical linked-cluster expansions (NLCE). First, I show universal thermodynamics of SU(N) Fermi-Hubbard models above superexchange temperatures. Then, I discuss the agreement between numerical simulated equations of state and correlation functions to optical lattice experiments using 173Yb [SU(N)-symmetric interactions] and three spin-flavors of 6Li [spin-dependent interactions] at intermediate temperatures. Thermometry performed with this method agrees well with the model-independent thermometry. Lastly, I propose a method of computing observables at low temperatures in bipartite ordered states by adding a suitable boundary field to the NLCE. NLCE agreeing to quantum simulations at temperatures above the superexchange temperatures and a possibility to make accurate predictions at low temperatures for certain states make it a powerful algorithm to be used side-by-side with quantum simulations. Chapter 7 is based on the observation of magnonic superradiance in ErFeO3. The spin Hamiltonian reveals a simultaneous kink and mode-softening of two of the lower polaritons, strongly suggesting a superradiant phase transition. Its mapping to an extended Dicke model is also discussed. This is the first evidence towards a macroscopically squeezed spin state. Finally, I conclude with a broad discussion and an outlook in Chapter 8.

•Aug 1, 2025•0 citations

Strings of ultracold molecules in a synthetic dimension

Bhuvanesh Sundar, Matthew Thibodeau, Zhiyuan Wang +2 more

We consider ultracold polar molecules trapped in a unit-filled one-dimensional chain in real space created with an optical lattice or a tweezer array and illuminated by microwaves that resonantly drive transitions within a chain of rotational states. We describe the system by a two-dimensional lattice model, with the first dimension being a lattice in real space and the second dimension being a lattice in a synthetic direction composed of rotational states. We calculate this system's ground-state phase diagram. We show that as the dipole interaction strength is increased, the molecules undergo a phase transition from a two-dimensional gas to a phase in which the molecules bind together and form a string that resembles a one-dimensional object living in the two-dimensional (i.e., one real and one synthetic dimensional) space. We demonstrate this with two complementary techniques: numerical calculations using matrix product state techniques and an analytic solution in the limit of infinitely strong dipole interaction. Our calculations reveal that the string phase at infinite interaction is effectively described by emergent particles living on the string and that this leads to a rich spectrum with excitations missed in earlier mean-field treatments.

arXiv:1812.02229•Physical Review A•Jan 25, 2019•23 citations

Probing topological edge states in a molecular synthetic dimension

Adarsh P. Raghuram, Francesca M. Blondell, Jonathan M. Mortlock +7 more

Engineering synthetic dimensions, where the physics of additional spatial dimensions is simulated within the internal states of a quantum system, allows the realisation of phenomena not otherwise accessible in experiments. Ultracold ground-state polar molecules are an ideal platform to encode synthetic dimensions, offering access to large Hilbert spaces of long-lived internal states associated with the rotational and hyperfine degrees of freedom, that can be coupled together with microwave fields to simulate tunnelling. Here, to benchmark the advantages of ultracold molecules, we encode a 1D synthetic lattice in the rotational states of ultracold RbCs molecules and use it to investigate the well-known Su-Schrieffer-Heeger (SSH) model, a minimal model displaying topological properties. To probe the system, we perform spectroscopy using an auxiliary rotational state and study the time dynamics after deterministic state preparation. We demonstrate long coherence times, typically ~500 times the lattice tunnelling period, even for a synthetic lattice using 8 rotational states. Observations of dynamics at long times with full site-resolved readout of the synthetic dimension allow us to test the effects of chiral and non-chiral perturbations on the topologically protected edge states. Our work lays the foundation for further quantum simulations using the rich internal structure of molecules, including dipolar string phases in interacting samples of molecules, and adiabatic state preparation of many-body Hamiltonians.

physics.atom-phCross-listedarXiv:2604.00745•Apr 2, 2026•0 citations
Synthetic-dimension platforms offer unique pathways for engineering quantum matter. We compute the phase diagram of a many-body system of ultracold atoms (or polar molecules) with a set of Rydberg states (or rotational states) as a synthetic dimension, where the particles are arranged in real space in optical microtrap arrays and interact via dipole-dipole exchange interaction. Using mean-field theory, we find three ordered phases---two are localized in the synthetic dimension, predicted as zero-temperature ground states by Sundar et al. [Sci. Rep. 8, 3422 (2018); Phys. Rev. A 99, 013624 (2019)], and one is a delocalized phase. We characterize them by identifying the spontaneously broken discrete symmetries of the Hamiltonian. We also compute the phase diagram as a function of temperature and interaction strength for both signs of the interaction. For system sizes with more than six synthetic sites and attractive interactions, we find that the thermal phase transitions can be first or second order, which leads to a tricritical point on the phase boundary. By examining the dependence of the tricritical point and other special points of the phase boundary on the synthetic dimension size, we shed light on the physics for thermodynamically large synthetic dimension.
We calculate properties of dipolar interacting ultracold molecules or Rydberg atoms in a semisynthetic three-dimensional configuration---one synthetic dimension plus a two-dimensional real-space optical lattice or periodic microtrap array---using the stochastic Green's function quantum Monte Carlo method. Through a calculation of thermodynamic quantities and appropriate correlation functions, along with their finite-size scalings, we show that there is a second-order transition to a low-temperature phase in which two-dimensional ``sheets'' form in the synthetic dimension of internal rotational or electronic states of the molecules or Rydberg atoms, respectively. Simulations for different values of the interaction VVV, which acts between atoms or molecules that are adjacent both in real and synthetic space, allow us to compute a phase diagram. We find a finite-temperature transition at sufficiently large VVV as well as a quantum phase transition---a critical value Vc{V}_{c}Vc​ below which the transition temperature vanishes.
Synthetic dimensions alter one of the most fundamental properties in nature, the dimension of space. They allow, for example, a real three-dimensional system to act as effectively four-dimensional. Driven by such possibilities, synthetic dimensions have been engineered in ongoing experiments with ultracold matter. We show that rotational states of ultracold molecules can be used as synthetic dimensions extending to many - potentially hundreds of - synthetic lattice sites. Microwaves coupling rotational states drive fully controllable synthetic inter-site tunnelings, enabling, for example, topological band structures. Interactions leads to even richer behavior: when molecules are frozen in a real space lattice with uniform synthetic tunnelings, dipole interactions cause the molecules to aggregate to a narrow strip in the synthetic direction beyond a critical interaction strength, resulting in a quantum string or a membrane, with an emergent condensate that lives on this string or membrane. All these phases can be detected using local measurements of rotational state populations.
We introduce a classical analog of quantum matter in ultracold molecule -- or Rydberg atom -- synthetic dimensions, extending the Potts model to include interactions J1 between atoms adjacent in both real and synthetic space and studying its finite temperature properties. For intermediate values of J1, the resulting phases and phase diagrams are similar to those of the clock and Villain models, in which three phases emerge. There exists a sheet phase analogous to that found in quantum synthetic dimension models between the high temperature disordered phase and the low temperature ferromagnetic phase. We also employ machine learning to uncover non-trivial features of the phase diagram using the learning by confusion approach. The key result there is that the method is able to discern several successive phase transitions.
In this dissertation, I theoretically investigate the equilibrium properties of three strongly correlated multi-level quantum platforms -- synthetic dimension using ultracold Rydberg atoms, multi-flavor Fermi-Hubbard simulators with ultracold atoms, and magnon-spin coupled rare-earth orthoferrites -- using various numerical and analytical methods. After the broad research motivation in the first chapter, Chapter 2 introduces the general principles of quantum simulation using synthetic dimension platforms. Chapter 3 discusses the first realization with Rydberg atom platform to simulate the topological Su-Schrieffer-Heeger (SSH) model, and how environmental noise affects it. Chapter 4 shows the mean-field phase diagram of dipole-coupled ultracold Rydberg atom arrays exhibiting quantum strings and other ordered states. The connection of the thermal phase transition to that of a classical extended Potts model is also discussed from a renormalization (RG) and generalized duality perspective. These examples illustrate the versatility of synthetic dimension in simulating and engineering quantum phenomena. Chapters 5-6 explore the properties of multi-flavor Fermi-Hubbard models on square optical lattices using numerical linked-cluster expansions (NLCE). First, I show universal thermodynamics of SU(N) Fermi-Hubbard models above superexchange temperatures. Then, I discuss the agreement between numerical simulated equations of state and correlation functions to optical lattice experiments using 173Yb [SU(N)-symmetric interactions] and three spin-flavors of 6Li [spin-dependent interactions] at intermediate temperatures. Thermometry performed with this method agrees well with the model-independent thermometry. Lastly, I propose a method of computing observables at low temperatures in bipartite ordered states by adding a suitable boundary field to the NLCE. NLCE agreeing to quantum simulations at temperatures above the superexchange temperatures and a possibility to make accurate predictions at low temperatures for certain states make it a powerful algorithm to be used side-by-side with quantum simulations. Chapter 7 is based on the observation of magnonic superradiance in ErFeO3. The spin Hamiltonian reveals a simultaneous kink and mode-softening of two of the lower polaritons, strongly suggesting a superradiant phase transition. Its mapping to an extended Dicke model is also discussed. This is the first evidence towards a macroscopically squeezed spin state. Finally, I conclude with a broad discussion and an outlook in Chapter 8.
We consider ultracold polar molecules trapped in a unit-filled one-dimensional chain in real space created with an optical lattice or a tweezer array and illuminated by microwaves that resonantly drive transitions within a chain of rotational states. We describe the system by a two-dimensional lattice model, with the first dimension being a lattice in real space and the second dimension being a lattice in a synthetic direction composed of rotational states. We calculate this system's ground-state phase diagram. We show that as the dipole interaction strength is increased, the molecules undergo a phase transition from a two-dimensional gas to a phase in which the molecules bind together and form a string that resembles a one-dimensional object living in the two-dimensional (i.e., one real and one synthetic dimensional) space. We demonstrate this with two complementary techniques: numerical calculations using matrix product state techniques and an analytic solution in the limit of infinitely strong dipole interaction. Our calculations reveal that the string phase at infinite interaction is effectively described by emergent particles living on the string and that this leads to a rich spectrum with excitations missed in earlier mean-field treatments.
Engineering synthetic dimensions, where the physics of additional spatial dimensions is simulated within the internal states of a quantum system, allows the realisation of phenomena not otherwise accessible in experiments. Ultracold ground-state polar molecules are an ideal platform to encode synthetic dimensions, offering access to large Hilbert spaces of long-lived internal states associated with the rotational and hyperfine degrees of freedom, that can be coupled together with microwave fields to simulate tunnelling. Here, to benchmark the advantages of ultracold molecules, we encode a 1D synthetic lattice in the rotational states of ultracold RbCs molecules and use it to investigate the well-known Su-Schrieffer-Heeger (SSH) model, a minimal model displaying topological properties. To probe the system, we perform spectroscopy using an auxiliary rotational state and study the time dynamics after deterministic state preparation. We demonstrate long coherence times, typically ~500 times the lattice tunnelling period, even for a synthetic lattice using 8 rotational states. Observations of dynamics at long times with full site-resolved readout of the synthetic dimension allow us to test the effects of chiral and non-chiral perturbations on the topologically protected edge states. Our work lays the foundation for further quantum simulations using the rich internal structure of molecules, including dipolar string phases in interacting samples of molecules, and adiabatic state preparation of many-body Hamiltonians.