Vogt and Wannier [Phys. Rev. 95, 1190 (1954)] predicted that the capture rate of a polarizable neutral atom or molecule by an ion should increase by a factor of 2 compared to the classical Langevin rate as the collision energy approaches zero. This prediction has not been verified experimentally. The ${\mathrm{H}}_{2}^{+}$ $+$ ${\mathrm{H}}_{2}$ reaction is ideally suited to observe this effect because the small reduced mass makes quantum effects related to $s$ -wave scattering observable at higher collision energies than in other systems. Moreover, the reaction rate for this barrierless, strongly exothermic reaction follows the classical Langevin capture model down to cold-collision conditions (about ${k}_{\mathrm{B}}\ifmmode\times\else\texttimes\fi{}1$ K) and is not affected by short-range interactions. Below this temperature, a strong enhancement of the reaction rate resulting from charge--quadrupole interaction between ${\mathrm{H}}_{2}^{+}$ and ground-state ortho ${\mathrm{H}}_{2}$ ( $J=1$ ) was observed. Here we present an experimental study of the reaction of ${\mathrm{H}}_{2}^{+}$ and para ${\mathrm{H}}_{2}$ ( $J=0$ ), which has no dipole and no quadrupole moments, at collision energies below ${k}_{\mathrm{B}}\ifmmode\times\else\texttimes\fi{}1$ K. We observe an enhancement at the lowest collision energies which is attributed to the quantum enhancement predicted by Vogt and Wannier. Measurements of the reaction of ${\mathrm{HD}}^{+}$ with HD support this conclusion.Vogt and Wannier [Phys. Rev. 95, 1190 (1954)] predicted that the capture rate of a polarizable neutral atom or molecule by an ion should increase by a factor of 2 compared to the classical Langevin rate as the collision energy approaches zero. This prediction has not been verified experimentally. The ${\mathrm{H}}_{2}^{+}$ $+$ ${\mathrm{H}}_{2}$ reaction is ideally suited to observe this effect because the small reduced mass makes quantum effects related to $s$-wave scattering observable at higher collision energies than in other systems. Moreover, the reaction rate for this barrierless, strongly exothermic reaction follows the classical Langevin capture model down to cold-collision conditions (about ${k}_{\mathrm{B}}\ifmmode\times\else\texttimes\fi{}1$ K) and is not affected by short-range interactions. Below this temperature, a strong enhancement of the reaction rate resulting from charge--quadrupole interaction between ${\mathrm{H}}_{2}^{+}$ and ground-state ortho ${\mathrm{H}}_{2}$ ($J=1$) was observed. Here we present an experimental study of the reaction of ${\mathrm{H}}_{2}^{+}$ and para ${\mathrm{H}}_{2}$ ($J=0$), which has no dipole and no quadrupole moments, at collision energies below ${k}_{\mathrm{B}}\ifmmode\times\else\texttimes\fi{}1$ K. We observe an enhancement at the lowest collision energies which is attributed to the quantum enhancement predicted by Vogt and Wannier. Measurements of the reaction of ${\mathrm{HD}}^{+}$ with HD support this conclusion.

arXiv:2211.06290Physical Review ANov 14, 20225 citations

A Quantum-Mechanical Equation of Reaction Rates

Iwao Yasumori, Kenji Fueki

The Journal of Chemical PhysicsOct 1, 19548 citations

Controlling the repetition rate of a mode-locked laser using anf-deformed Bose–Einstein condensate

Zahra Haghshenasfard, Michael G Cottam

Investigations are made for the possibility of using an f-deformed Bose–Einstein condensate (BEC) inside the resonator of a mode-locked laser to achieve tunable control of the repetition rate. Slow light propagation of the probe field through the f-deformed BEC may lead to a large observable increase in the cavity round-trip delay and, therefore, to a reduction in the effective repetition rate of the laser. Conversely, negative propagation velocity through the f-deformed BEC can lead to a decrease in the cavity round-trip and to an increase in the effective repetition rate. Simulations are presented using an f-deformed BEC of Λ-type three-level atoms beyond the rotating wave approximation. Collisions between the atoms are considered as a special kind of f-deformation where the collision rate κ is regarded as the deformation parameter. In particular, it is found that the repetition rate can be controlled effectively by changing the collision rate κ, the total number of atoms N and the parameter λ for the counter-rotating terms.Investigations are made for the possibility of using an f-deformed Bose–Einstein condensate (BEC) inside the resonator of a mode-locked laser to achieve tunable control of the repetition rate. Slow light propagation of the probe field through the f-deformed BEC may lead to a large observable increase in the cavity round-trip delay and, therefore, to a reduction in the effective repetition rate of the laser. Conversely, negative propagation velocity through the f-deformed BEC can lead to a decrease in the cavity round-trip and to an increase in the effective repetition rate. Simulations are presented using an f-deformed BEC of Λ-type three-level atoms beyond the rotating wave approximation. Collisions between the atoms are considered as a special kind of f-deformation where the collision rate κ is regarded as the deformation parameter. In particular, it is found that the repetition rate can be controlled effectively by changing the collision rate κ, the total number of atoms N and the parameter λ for the counter-rotating terms.

Journal of Physics B Atomic Molecular and Optical PhysicsDec 16, 20111 citation

Probability flow in multi-step reactions

William A. Friedman

Springer eBooksApr 7, 20080 citations

Quantum information scrambling and chemical reactions

Chenghao Zhang, Sohang Kundu, Nancy Makri +2 more

The ultimate regularity of quantum mechanics creates a tension with the assumption of classical chaos used in many of our pictures of chemical reaction dynamics. Out-of-time-order correlators (OTOCs) provide a quantum analog to the Lyapunov exponents that characterize classical chaotic motion. Maldacena, Shenker, and Stanford have suggested a fundamental quantum bound for the rate of information scrambling, which resembles a limit suggested by Herzfeld for chemical reaction rates. Here, we use OTOCs to study model reactions based on a double-well reaction coordinate coupled to anharmonic oscillators or to a continuum oscillator bath. Upon cooling, as one enters the tunneling regime where the reaction rate does not strongly depend on temperature, the quantum Lyapunov exponent can approach the scrambling bound and the effective reaction rate obtained from a population correlation function can approach the Herzfeld limit on reaction rates: Tunneling increases scrambling by expanding the state space available to the system. The coupling of a dissipative continuum bath to the reaction coordinate reduces the scrambling rate obtained from the early-time OTOC, thus making the scrambling bound harder to reach, in the same way that friction is known to lower the temperature at which thermally activated barrier crossing goes over to the low-temperature activationless tunneling regime. Thus, chemical reactions entering the tunneling regime can be information scramblers as powerful as the black holes to which the quantum Lyapunov exponent bound has usually been applied.The ultimate regularity of quantum mechanics creates a tension with the assumption of classical chaos used in many of our pictures of chemical reaction dynamics. Out-of-time-order correlators (OTOCs) provide a quantum analog to the Lyapunov exponents that characterize classical chaotic motion. Maldacena, Shenker, and Stanford have suggested a fundamental quantum bound for the rate of information scrambling, which resembles a limit suggested by Herzfeld for chemical reaction rates. Here, we use OTOCs to study model reactions based on a double-well reaction coordinate coupled to anharmonic oscillators or to a continuum oscillator bath. Upon cooling, as one enters the tunneling regime where the reaction rate does not strongly depend on temperature, the quantum Lyapunov exponent can approach the scrambling bound and the effective reaction rate obtained from a population correlation function can approach the Herzfeld limit on reaction rates: Tunneling increases scrambling by expanding the state space available to the system. The coupling of a dissipative continuum bath to the reaction coordinate reduces the scrambling rate obtained from the early-time OTOC, thus making the scrambling bound harder to reach, in the same way that friction is known to lower the temperature at which thermally activated barrier crossing goes over to the low-temperature activationless tunneling regime. Thus, chemical reactions entering the tunneling regime can be information scramblers as powerful as the black holes to which the quantum Lyapunov exponent bound has usually been applied.

Proceedings of the National Academy of SciencesApr 1, 202413 citations

{\mathrm{H}}_{2}^{+}

+

{\mathrm{H}}_{2}

reaction is ideally suited to observe this effect because the small reduced mass makes quantum effects related to

s

-wave scattering observable at higher collision energies than in other systems. Moreover, the reaction rate for this barrierless, strongly exothermic reaction follows the classical Langevin capture model down to cold-collision conditions (about ${k}_{\mathrm{B}}\ifmmode\times\else\texttimes\fi{}1$ K) and is not affected by short-range interactions. Below this temperature, a strong enhancement of the reaction rate resulting from charge--quadrupole interaction between

{\mathrm{H}}_{2}^{+}

and ground-state ortho

{\mathrm{H}}_{2}

(

J=1

) was observed. Here we present an experimental study of the reaction of

{\mathrm{H}}_{2}^{+}

and para

{\mathrm{H}}_{2}

(

J=0

), which has no dipole and no quadrupole moments, at collision energies below ${k}_{\mathrm{B}}\ifmmode\times\else\texttimes\fi{}1$ K. We observe an enhancement at the lowest collision energies which is attributed to the quantum enhancement predicted by Vogt and Wannier. Measurements of the reaction of

{\mathrm{HD}}^{+}

with HD support this conclusion.