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arXiv:2204.04595 · Chinese Physics Letters

Analogue Black Holes in Reactive Molecules

Ren Zhang, Chenwei Lv, Qi Zhou

Published Apr 1, 2023• 0 citations
arXivHTMLPDF

Abstract

We show that reactive molecules with a unit probability of reaction naturally provide a simulator of some intriguing black hole physics. The unit reaction at the short distance acts as an event horizon and delivers a one-way traffic for matter waves passing through the potential barrier when two molecules interact by high partial-wave scatterings or dipole-dipole interactions. In particular, the scattering rate as a function of the incident energy exhibits a thermal-like distribution near the maximum of the interaction energy in the same manner as a scalar field scatters with the potential barrier outside the event horizon of a black hole. Such a thermal-like scattering can be extracted from the temperature-dependent two-body loss rate measured in experiments on KRb and other molecules.

DOI
10.1088/0256-307x/40/5/050401

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We show that reactive molecules with a unit probability of reaction naturally provide a simulator of some intriguing black hole physics. The unit reaction at the short distance acts as an event horizon and delivers a one-way traffic for matter waves passing through the potential barrier when two molecules interact by high partial-wave scatterings or dipole-dipole interactions. In particular, the scattering rate as a function of the incident energy exhibits a thermal-like distribution near the maximum of the interaction energy in the same manner as a scalar field scatters with the potential barrier outside the event horizon of a black hole. Such a thermal-like scattering can be extracted from the temperature-dependent two-body loss rate measured in experiments on KRb and other molecules.
Black holes permit matter to cross their event horizon in only one direction. We show that interacting bosons in optical lattices with asymmetric barrier exhibit an analogous phenomenon, creating unidirectional quantum transport without external driving or dissipation. This directionality emerges purely from many-body interactions, which cause asymmetric projection of the initial state onto transport-enabled or transport-forbidden sectors. The resulting dynamics create an effective one-way boundary in Hilbert space, forming a quantum analog of a black-hole event horizon. Our results establish interactions as a fundamentally new route to directional transport, enabling coherent rectification in atomtronic circuits by the use of intrinsic properties of the system only.
How does a chemical reaction proceed at ultralow temperatures? Can simple quantum mechanical rules such as quantum statistics, single partial-wave scattering, and quantum threshold laws provide a clear understanding of the molecular reactivity under a vanishing collision energy? Starting with an optically trapped near-quantum-degenerate gas of polar 40K87Rb molecules prepared in their absolute ground state, we report experimental evidence for exothermic atom-exchange chemical reactions. When these fermionic molecules were prepared in a single quantum state at a temperature of a few hundred nanokelvin, we observed p-wave-dominated quantum threshold collisions arising from tunneling through an angular momentum barrier followed by a short-range chemical reaction with a probability near unity. When these molecules were prepared in two different internal states or when molecules and atoms were brought together, the reaction rates were enhanced by a factor of 10 to 100 as a result of s-wave scattering, which does not have a centrifugal barrier. The measured rates agree with predicted universal loss rates related to the two-body van der Waals length.
The realization of ultracold polar molecules in laboratories has pushed physics and chemistry to new realms. In particular, these polar molecules offer scientists unprecedented opportunities to explore chemical reactions in the ultracold regime where quantum effects become profound. However, a key question about how two-body losses depend on quantum correlations in interacting many-body systems remains open so far. Here, we present a number of universal relations that directly connect two-body losses to other physical observables, including the momentum distribution and density correlation functions. These relations, which are valid for arbitrary microscopic parameters, such as the particle number, the temperature, and the interaction strength, unfold the critical role of contacts, a fundamental quantity of dilute quantum systems, in determining the reaction rate of quantum reactive molecules in a many-body environment. Our work opens the door to an unexplored area intertwining quantum chemistry; atomic, molecular, and optical physics; and condensed matter physics.
We present a unified formalism for describing chemical reaction rates of trapped, ultracold molecules. This formalism reduces the scattering to its essential features, namely, a propagation of the reactant molecules through a gauntlet of long-range forces before they ultimately encounter one another, followed by a probability for the reaction to occur once they do. In this way, the electric-field dependence should be readily parametrized in terms of a pair of fitting parameters (along with a C6{C}_{6}C6​ coefficient) for each asymptotic value of partial-wave quantum numbers $|L,{M}_{L}\ensuremath{\rangle}$. From this, the electric-field dependence of the collision rates follows automatically. We present examples for reactive species, such as KRb, and nonreactive species, such as RbCs.
We propose an analogy between the quantum physics of a black hole in its late stages of the evaporation process and a superfluid Bose-Einstein condensate (BEC), based on the Horowitz and Maldacena quantum final-state projection model [J. High Energy Phys. 02 (2004), 008]. The superfluid region is considered to be analogous to the interior of a black hole, and the normal fluid/superfluid interface is compared to the event horizon of a black hole. We theoretically investigate the possibility of recovering the wave function of particles incident on a superfluid BEC from the normal fluid, facilitated by the mode conversion processes occurring at the normal fluid/superfluid BEC interface. We also study how the correlations of an infalling mode with an external memory system can be preserved in the process, similar to Hayden and Preskill's ``information mirror'' model for a black hole [J. High Energy Phys. 09 (2007), 120]. Based on these analogies, we conjecture that the quantum state of bosons entering a black hole in its final state is the superfluid quantum ground state of interacting bosons. Our analogy suggests that the wave function of bosons falling into a black hole can be recovered from the outgoing Hawking modes. In the particular case in which a holelike quasiparticle (a density dip) is incident on the superfluid BEC causing the superfluid to shrink in size, our model indicates that the evaporation is unitary.
The quantum description of a black hole predicts that quantum information hidden behind the event horizon can be teleported outside almost instantaneously. In this work, we demonstrate that a chiral spin-chain model, which naturally simulates a binary black hole system, can realise this teleportation process. Our system captures two essential components of this protocol: Hawking radiation, which generates the necessary entanglement between the black holes, and optimal scrambling, which enables high-fidelity teleportation on short timescales. Through numerical simulations, we quantify the key timescales governing the process, including the Page time, radiation time, scrambling time, and butterfly velocity, showing their universal dependence on the chiral coupling strength. Our results establish the feasibility of simulating quantum properties of black holes within condensed matter systems, offering an experimentally accessible platform for probing otherwise inaccessible high-energy phenomena.