Experimentally Accessible Invariants Encoded in Interparticle Correlations of Harmonically Trapped Ultra-cold Few-Fermion Mixtures

Pęcak, Daniel; Gajda, Mariusz; Sowiński, Tomasz

doi:10.1007/s00601-017-1321-3

Cited by 9 publications

(11 citation statements)

References 67 publications

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“…The physically relevant information about the scattering length comes exclusively from the cusp of the Jastrow factor near the coalescence point. The long-range behavior is an artifact from the definition (10). Since the longrange part of the correlation factor is smooth, however, it is easier to correct it with the Fock-space expansion of the transcorrelated wave function Φ.…”

Section: B Correlation Factor For 1d System With Contact Interactionmentioning

confidence: 99%

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Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions

et al. 2018

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Exact diagonalization expansions of Bose or Fermi gases with contact interactions converge very slowly due to a nonanalytic cusp in the wave function. Here we develop a transcorrelated approach where the cusp is treated exactly and folded into the many-body Hamiltonian with a similarity transformation that removes the leading-order singularity. The resulting transcorrelated Hamiltonian is not Hermitian but can be treated numerically with a standard projection approach. The smoothness of the wave function improves by at least one order and thus the convergence rate for the ground-state energy improves. By numerical investigation of a one-dimensional gas of spin-1 2 fermions we find the error in the transcorrelated energy to scale as M −3 with a single-particle basis of M plane waves compared to M −1 for the expansion of the original Hamiltonian and M −2 using conventional lattice renormalization.

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Section: B Correlation Factor For 1d System With Contact Interactionmentioning

confidence: 99%

“…(49); "tcorr": transcorrelated Hamiltonian of Eq. (45); "kc" truncation parameter for fixed correlation factor of Eq (10)…”

mentioning

confidence: 99%

Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions

et al. 2018

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“…Fermions of opposite flavors are fundamentally distinguishable and may have the same or different masses (in the following we denote the mass ratio µ = m ↑ /m ↓ ). The Hamiltonian of the mass-imbalanced system reads (see [54][55][56]):…”

Section: The Modelmentioning

confidence: 99%

Global optimization for quantum dynamics of few-fermion systems

Pęcak

Sowiński

et al. 2018

Phys. Rev. A

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Quantum state preparation is vital to quantum computation and quantum information processing tasks. In adiabatic state preparation, the target state is theoretically obtained with nearly perfect fidelity if the control parameter is tuned slowly enough. As this, however, leads to slow dynamics, it is often desirable to be able to do processes faster. In this work, we employ two global optimization methods to estimate the quantum speed limit for few-fermion systems confined in a one-dimensional harmonic trap. Such systems can be produced experimentally in a well controlled manner. We determine the optimized control fields and achieve a reduction in the ramping time of more than a factor of four compared to linear ramping. We also investigate how robust the fidelity is to small variations of the control fields away from the optimized shapes.

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“…Another important mixed system is the unequal mass case [72][73][74][75][76]. Some recent results have demonstrated a phase separation in the light component for Fermi-Fermi mixtures [75], which can also be seen for a single heavy impurity in a light Bose system [74].…”

Section: Mixed Systemsmentioning

confidence: 99%

“…Some recent results have demonstrated a phase separation in the light component for Fermi-Fermi mixtures [75], which can also be seen for a single heavy impurity in a light Bose system [74]. In fact, the case of a single impurity in a Bose gas is often called the 'Bose polaron' problem and is much studied at present in the few-body limit [73,74,76].…”

Section: Mixed Systemsmentioning

confidence: 99%

Exploring the few- to many-body crossover using cold atoms in one dimension

Zinner

2016

EPJ Web of Conferences

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Abstract. Cold atomic gases have provided us with a great number of opportunities for studying various physical systems under controlled conditions that are seldom offered in other fields. We are thus at the point where one can truly do quantum simulation of models that are relevant for instance in condensed-matter or high-energy physics, i.e. we are on the verge of a 'cool' quantum simulator as envisioned by Feynman. One of the avenues under exploration is the physics of one-dimensional systems. Until recently this was mostly in the many-body limit but now experiments can be performed with controllable particle numbers all the way down to the few-body regime. After a brief introduction to some of the relevant experiments, I will review recent theoretical work on one-dimensional quantum systems containing bosons, fermions, or mixtures of the two, with a particular emphasis on the case where the particles are held by an external trap.

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Experimentally Accessible Invariants Encoded in Interparticle Correlations of Harmonically Trapped Ultra-cold Few-Fermion Mixtures

Cited by 9 publications

References 67 publications

Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions

Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions

Global optimization for quantum dynamics of few-fermion systems

Exploring the few- to many-body crossover using cold atoms in one dimension

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