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Currently laser cooling schemes are fundamentally based on the weak coupling regime. This requirement sets the trap frequency as an upper bound to the cooling rate. In this work we present a numerical study that shows the feasibility of cooling in the strong coupling regime which then allows cooling rates that are faster than the trap frequency with state of the art experimental parameters. The scheme we present can work for trapped atoms or ions as well as mechanical oscillators. It can also cool medium size ions chains close to the ground state.
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Simulation of fermionic many-body systems on a quantum computer requires a suitable encoding of fermionic degrees of freedom into qubits. Here we revisit the Superfast Encoding introduced by Kitaev and one of the authors. This encoding maps a target fermionic Hamiltonian with two-body interactions on a graph of degree $d$ to a qubit simulator Hamiltonian composed of Pauli operators of weight $O(d)$. A system of $m$ fermi modes gets mapped to $n=O(md)$ qubits. We propose Generalized Superfast Encodings (GSE) which require the same number of qubits as the original one but have more favorable properties. First, we describe a GSE such that the corresponding quantum code corrects any single-qubit error provided that the interaction graph has degree $dge 6$. In contrast, we prove that the original Superfast Encoding lacks the error correction property for $dle 6$. Secondly, we describe a GSE that reduces the Pauli weight of the simulator Hamiltonian from $O(d)$ to $O(log{d})$. The robustness against errors and a simplified structure of the simulator Hamiltonian offered by GSEs can make simulation of fermionic systems within the reach of near-term quantum devices. As an example, we apply the new encoding to the fermionic Hubbard model on a 2D lattice.
Recent high-precision measurements of nuclear deep inelastic scattering at high x and moderate 6 < Q$^2$ < 9GeV$^2$ give a rare opportunity to reach the quark distributions in the {it superfast} region, in which the momentum fraction of the nucleon carried by its constituent quark is larger than the total fraction of the nucleon at rest, x>1. We derive the leading-order QCD evolution equation for such quarks with the goal of relating the moderate-Q$^2$ data to the two earlier measurements of superfast quark distributions at large 60 < Q$^2$ < 200~GeV$^2$. Since the high-Q$^2$ measurements gave strongly contradictory estimates of the nuclear effects that generate superfast quarks, relating them to the high-precision, moderate-Q$^2$ data through QCD evolution allows us to clarify this longstanding issue. Our calculations indicate that the moderate-Q$^2$ data at $xlesssim 1.05$ are in better agreement with the high-Q$^2$ data measured in (anti)neutrino-nuclear reactions which require substantial high-momentum nuclear effects in the generation of superfast quarks. Our prediction for the high-Q$^2$ and x>1.1 region is somewhat in the middle of the neutrino-nuclear and muon-nuclear scattering data.
Ruelle predicted that the maximal amplification of perturbations in homogeneous isotropic turbulence is exponential $e^{sigma sqrt{Re} t}$ (where $sigma sqrt{Re}$ is the maximal Liapunov exponent). In our earlier works, we predicted that the maximal amplification of perturbations in fully developed turbulence is faster than exponential $e^{sigma sqrt{Re} sqrt{t} +sigma_1 t}$. That is, we predicted superfast initial amplification of perturbations. Built upon our earlier numerical verification of our prediction, here we conduct a large numerical verification with resolution up to $2048^3$ and Reynolds number up to $6210$. Our direct numerical simulation here confirms our analytical prediction. Our numerical simulation also demonstrates that such superfast amplification of perturbations leads to superfast nonlinear saturation. We conclude that such superfast amplification and superfast nonlinear saturation of ever existing perturbations serve as the mechanism for the generation, development and persistence of fully developed turbulence.
We propose a quantum information based scheme to reduce the temperature of quantum many-body systems, and access regimes beyond the current capability of conventional cooling techniques. We show that collective measurements on multiple copies of a system at finite temperature can simulate measurements of the same system at a lower temperature. This idea is illustrated for the example of ultracold atoms in optical lattices, where controlled tunnel coupling and quantum gas microscopy can be naturally combined to realize the required collective measurements to access a lower, virtual temperature. Our protocol is experimentally implemented for a Bose-Hubbard model on up to 12 sites, and we successfully extract expectation values of observables at half the temperature of the physical system. Additionally, we present related techniques that enable the extraction of zero-temperature states directly.
We introduce a method for digital preparation of ground states of a simulated Hamiltonians, inspired by cooling in nature and adapted to leverage the capabilities of digital quantum hardware. The cold bath is simulated by a single ancillary qubit, which is reset periodically and coupled to the system non-perturbatively. Studying this cooling method on a 1-qubit system toy model allows us to optimize two cooling protocols based on weak-coupling and strong-coupling approaches. Extending the insight from the 1-qubit system model, we develop two scalable protocols for larger systems. The LogSweep protocol extends the weak-coupling approach by sweeping energies to resonantly match any targeted transition. It demonstrates the ability to prepare an approximate ground state of tranverse-field Ising chains in the ferromangetic and critical phases, with an error that can be made polynomially small in time. The BangBang protocol extends the strong-coupling approach, and exploits a heuristics for local Hamiltonians to maximise the probability of de-exciting system transitions in the shortest possible time. Although this protocol does not promise long-time convergence, it allows for a rapid cooling to an approximation of the ground state, making this protocol appealing for near-term simulation applications.
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