Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning
$^{87}{\rm Rb}$ 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-l...
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| Format: | Article |
| Language: | English |
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SciPost
2023-01-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.14.1.004 |
| _version_ | 1797951683970465792 |
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| author | Madhumita Sarkar, Mainak Pal, Arnab Sen, Krishnendu Sengupta |
| author_facet | Madhumita Sarkar, Mainak Pal, Arnab Sen, Krishnendu Sengupta |
| author_sort | Madhumita Sarkar, Mainak Pal, Arnab Sen, Krishnendu Sengupta |
| collection | DOAJ |
| description | $^{87}{\rm Rb}$ 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. |
| first_indexed | 2024-04-10T22:34:28Z |
| format | Article |
| id | doaj.art-cfd7fb930e3144a18b24a698f023ae44 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-04-10T22:34:28Z |
| publishDate | 2023-01-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-cfd7fb930e3144a18b24a698f023ae442023-01-16T14:50:39ZengSciPostSciPost Physics2542-46532023-01-0114100410.21468/SciPostPhys.14.1.004Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuningMadhumita Sarkar, Mainak Pal, Arnab Sen, Krishnendu Sengupta$^{87}{\rm Rb}$ 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.https://scipost.org/SciPostPhys.14.1.004 |
| spellingShingle | Madhumita Sarkar, Mainak Pal, Arnab Sen, Krishnendu Sengupta Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning SciPost Physics |
| title | Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning |
| title_full | Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning |
| title_fullStr | Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning |
| title_full_unstemmed | Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning |
| title_short | Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning |
| title_sort | quantum order by disorder induced phase transition in rydberg ladders with staggered detuning |
| url | https://scipost.org/SciPostPhys.14.1.004 |
| work_keys_str_mv | AT madhumitasarkarmainakpalarnabsenkrishnendusengupta quantumorderbydisorderinducedphasetransitioninrydbergladderswithstaggereddetuning |