<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>-wave superfluidity in optical lattices of ultracold polar molecules

Kuns, K.; Rey, Ana María; Gorshkov, Alexey V.

doi:10.1103/physreva.84.063639

Cited by 29 publications

(20 citation statements)

References 73 publications

(177 reference statements)

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“…[490] predicted a ferroelectric phase, arising due to dipole-dipole interactions in an ensemble of ultracold polar molecules. [491] have shown that molecules can realize d−wave superfluid phases. [492] proposed a technique to prepare spin crystals of ultracold molecules non-adiabatically, bypassing the usual Kibble-Zurek scaling.…”

Section: Quantum Simulation With Rotational States In Dipolar Gasesmentioning

confidence: 99%

Quantum control of molecular rotation

2019

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The angular momentum of molecules, or, equivalently, their rotation in three-dimensional space, is ideally suited for quantum control. Molecular angular momentum is naturally quantized, time evolution is governed by a well-known Hamiltonian with only a few accurately known parameters, and transitions between rotational levels can be driven by external fields from various parts of the electromagnetic spectrum. Control over the rotational motion can be exerted in one-, two-and many-body scenarios, thereby allowing to probe Anderson localization, target stereoselectivity of bimolecular reactions, or encode quantum information, to name just a few examples. The corresponding approaches to quantum control are pursued within separate, and typically disjoint, subfields of physics, including ultrafast science, cold collisions, ultracold gases, quantum information science, and condensed matter physics. It is the purpose of this review to present the various control phenomena, which all rely on the same underlying physics, within a unified framework. To this end, we recall the Hamiltonian for free rotations, assuming the rigid rotor approximation to be valid, and summarize the different ways for a rotor to interact with external electromagnetic fields. These interactions can be exploited for control -from achieving alignment, orientation, or laser cooling in a one-body framework, steering bimolecular collisions, or realizing a quantum computer or quantum simulator in the many-body setting. IntroductionMolecules, unlike atoms, are extended objects that possess a number of different types of internal motion. In particular, the geometric arrangement of their constituent atoms endows molecules with the basic capability to rotate in three-dimensional space. Rotations can couple to vibrations of the atomic nuclei as well as to the orbital and spin angular momentum of the electrons. The resulting complexity of the energy level structure [1,2,3,4] may be daunting. It offers, on the other hand, a variety of knobs for control and thus is at the core of numerous applications, from the classic example of the ammonia maser [5] all the way to recent measurements of the electron's electric dipole moment in a cryogenic molecular beam of thorium monoxide [6].A key advantage of internal degrees of freedom such as rotation is that they occupy the low-energy part of the energy spectrum. Quantization of the rotational motion has been an early hallmark of quantum mechanics due to its connection to selection rules that govern all light-matter interactions [7]. Nowadays, rotational states and rotational molecular dynamics feature prominently in all active areas of AMO physics research as well as in neighbouring fields such as physical chemistry and quantum information science. Control over the rotational motion is crucial in one-body, two-body and many-body scenarios. For example, rotational state-selective excitation could pave the way towards separating left-and right handed enantiomers of chiral molecules [8,9]. Still within the one-body scenar...

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Section: Quantum Simulation With Rotational States In Dipolar Gasesmentioning

confidence: 99%

Quantum control of molecular rotation

2019

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“…Second, and perhaps more importantly, the anisotropic and long-range nature of the interaction allows for the realization of novel quantum phases, especially when the spatial dimensions of the system can be varied with optical lattices. Some of these engineered systems may find relevance to outstanding problems in condensed-matter physics [13,14]; moreover, qualitatively new types of physics can emerge in the presence of long-range interactions [15,16,17,18,19,20,21]. As a specific example of a unique feature of long-range interactions, a spin-1/2 Hamiltonian can be encoded based on a pair of oppositeparity rotational states where dipolar interactions give rise to a direct spin exchange coupling between molecules [22,23].…”

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confidence: 99%

New frontiers for quantum gases of polar molecules

et al. 2016

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The field of ultracold quantum matter has burgeoned over the last few decades, thanks to the growing capabilities for atomic systems to be probed and manipulated with exquisite control. Researchers can now precisely create and study quantum manybody states that are effectively isolated from the external environment. Much of the work in ultracold matter has focused on systems of alkali or alkaline-earth atoms, mainly due to their ease of cooling. Extending this precise control to molecules has seen rapidly increasing interest and activity, as molecules possess additional degrees of freedom that make them useful for tests of fundamental physics, studying ultracold chemistry and collisions, and engineering qualitatively new types of quantum phases and quantum many-body systems. Here, we review one particularly fruitful research direction: the creation and manipulation of ultracold bialkali molecules. The recent success in creating a quantum gas of polar molecules opens many exciting research opportunities. Atomic, Molecular, and Optical (AMO) systems offer experimentalists the ability to precisely control interactions in a quantum many-body system [1,2], and a rich set of experiments has already been performed. Some prominent examples include studies of the BEC-BCS crossover in two-component Fermi gases [3,4,5] and the superfluid-Mott insulator transition in ultracold bosons loaded into a 3D optical lattice [6]. Neutral atomic systems normally have point-like contact interactions that can be parametrized with a single quantity, the scattering length a, which can be tuned via a Feshbach resonance [2]. In recent years, systems with long-range and anisotropic interactions have garnered much attention. One natural example is the dipolar interaction between polar molecules, which is the focus of this Review. Of course, many other experimental platforms are also being pursued that feature long-range interactions, including highly magnetic atoms [7,8], trapped ions The dipolar interaction exhibits several important attributes. First, the energy scales in dipolar systems are usually much larger than those in typical atomic alkali systems, making it easier to study interaction-driven structural properties and non-equilibrium dynamics. Second, and perhaps more importantly, the anisotropic and long-range nature of the interaction allows for the realization of novel quantum phases, especially when the spatial dimensions of the system can be varied with optical lattices. Some of these engineered systems may find relevance to outstanding problems in condensed-matter physics [13,14]; moreover, qualitatively new types of physics can emerge in the presence of long-range interactions [15,16,17,18,19,20,21]. As a specific example of a unique feature of long-range interactions, a spin-1/2 Hamiltonian can be encoded based on a pair of oppositeparity rotational states where dipolar interactions give rise to a direct spin exchange coupling between molecules [22,23]. With this scheme implemented in an optical lattice, many-body spin dynam...

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“…Having obtained a matrix representation of the symmetry operatorsP R on the particle number sector (N ↑ , N ↓ ), we can decompose this subspace of Hilbert space further into the irreducible invariant subspaces of D 4 via the projection operator technique 42 (see also 40 for a detailed discussion). In the decomposition of a reducible representation the n-th irreducible representation occurs a n times, given by 42…”

Section: Acknowledgmentsmentioning

confidence: 99%

Quantum state tomography on a plaquette in the two-dimensional Hubbard model

Humeniuk

2019

Phys. Rev. B

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Motivated by recent quantum gas microscope experiments for fermions in optical lattices, we present proof of principle calculations showing that it is possible to obtain the complete information about the quantum state on a small subsystem from equilibrium determinantal quantum Monte Carlo simulations. Both diagonal (in the occupation number basis) and off-diagonal elements of the reduced density matrix are calculated for a square plaquette, which is embedded in a much larger system of the two-dimensional Hubbard model, both at half filling and in the doped case. The diagonalization of the reduced density matrix is done by exploiting the point group symmetry and particle number conservation, which allows to attach symmetry labels to its eigenvalues.Knowledge of the probabilities of plaquette occupation number configurations is useful for meticulous benchmarking of quantum gas microscope experiments. As the quantum state on the plaquette is exact and self-consistently embedded in an exact, correlated bath, the present approach connects to various cluster approximation techniques. arXiv:1907.12434v2 [cond-mat.str-el]

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d-wave superfluidity in optical lattices of ultracold polar molecules

Cited by 29 publications

References 73 publications

Quantum control of molecular rotation

Quantum control of molecular rotation

New frontiers for quantum gases of polar molecules

Quantum state tomography on a plaquette in the two-dimensional Hubbard model

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