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Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning
by Madhumita Sarkar, Mainak Pal, Arnab Sen, K. Sengupta
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Arnab Sen · Krishnendu Sengupta |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2204.12515v4 (pdf) |
| Date accepted: | 2022-09-20 |
| Date submitted: | 2022-09-13 04:20 |
| Submitted by: | Sengupta, Krishnendu |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
$^{87}{\rm Rb}$ atoms are known to have long-lived Rydberg excited states with controllable excitation amplitude (detuning) and strong repulsive van der Waals interaction $V_{{\bf r} {\bf r'}}$ between excited atoms at sites ${\bf r}$ and ${\bf r'}$. Here we study such atoms in a two-leg ladder geometry in the presence of both staggered and uniform detuning with amplitudes $\Delta$ and $\lambda$ respectively. We show that when $V_{{\bf r r'}} \gg(\ll) \Delta, \lambda$ for $|{\bf r}-{\bf r'}|=1(>1)$, these ladders host a plateau for a wide range of $\lambda/\Delta$ where the ground states are selected by a quantum order-by-disorder mechanism from a macroscopically degenerate manifold of Fock states with fixed Rydberg excitation density $1/4$. Our study further unravels the presence of an emergent Ising transition stabilized via the order-by-disorder mechanism inside the plateau. We identify the competing terms responsible for the transition and estimate a critical detuning $\lambda_c/\Delta=1/3$ which agrees well with exact-diagonalization based numerical studies. We also study the fate of this transition for a realistic interaction potential $V_{{\bf r} {\bf r'}} = V_0 /|{\bf r}-{\bf r'}|^6$, demonstrate that it survives for a wide range of $V_0$, and provide analytic estimate of $\lambda_c$ as a function of $V_0$. This allows for the possibility of a direct verification of this transition in standard experiments which we discuss.
List of changes
1) Added the line " "The amplitude of realizing a Rydberg
excitation at any site of such a chain can be controlled by changing the detuning, i.e, the difference
between the energy (frequency) of the external laser and the energy gap between the ground and
excited states of a Rydberg atom" on Pg 1 para 2.
2) Changed " " Here λ and ∆ denote the amplitudes of uniform and staggered detuning respectively, and w > 0 denotes the coupling strength between the Rydberg ground and excited states."
to
In Eq. 1, λ and ∆ denote the amplitudes of uniform and staggered
detuning such that λ + ∆ and λ − ∆ represent the energy differences between the energy of the
applied external laser and the energy gap between ground and excited Rydberg atomic levels on
even and odd sites respectively. Here w > 0 denotes the coupling strength between the Rydberg
ground and excited states. In an experimental setup, this coupling is controlled by two-photon
processes having Rabi frequency w/ħ [25–28]."
below Eq 1 in Sec 2.
3) Added Ref 67 which is
A. W. Glaetzle, M. Dalmonte, R. Nath, I. Rousochatzakis, R. Moessner and P. Zoller,
Quantum spin-ice and dimer models with rydberg atoms, Phys. Rev. X 4, 041037 (2014),
doi:10.1103/PhysRevX.4.041037.
Published as SciPost Phys. 14, 004 (2023)