arXiv:1207.2239

Impurity effects on the quantum coherence of a few-boson system

Pei Lu, Zhihai Zhang, Shiping Feng, Shi-Jie Yang

Published Jul 10, 2012• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.1207.2239

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arXiv:1207.2239

Impurity effects on the quantum coherence of a few-boson system

Pei Lu, Zhihai Zhang, Shiping Feng, Shi-Jie Yang

Published Jul 10, 2012• 0 citations

arXiv HTML PDF

Abstract

U_{BF}/U_{BB}

of the boson-fermion versus the boson-boson interactions plays a key role in the coherence revivals. As the average filling of the impurity increases, the coherence revivals remain nearly unaffected for

U_{BF}/U_{BB}=z

(

z\in Z

is an integer) while the odd revival peaks are damped for

U_{BF}/U_{BB}=z+1/2

, in agreement with the experimental observations. For unpolarized fermionic impurities, the coherence revivals are irrelevant to the strength of the fermion-fermion interactions.

DOI: 10.48550/arxiv.1207.2239

Related papers

Effect of fermionic impurities on the quantum coherence of a few-boson system

Pei Lu, Zhihai Zhang, Shiping Feng +1 more

The impurity effects on the quantum coherence of a few-boson system are studied within the two-site Hubbard model. Periodical collapses and revivals of coherence occur in the presence of either polarized or unpolarized fermionic impurities. The relative strength ${U}_{BF}/{U}_{BB}$ of the boson-fermion interaction versus the boson-boson interaction plays a key role in the coherence revivals. As the average filling of the impurity increases, the coherence revivals remain nearly unaffected for ${U}_{BF}/{U}_{BB}=z$ ($z\ensuremath{\in}Z$ is an integer) while the odd revival peaks are damped for ${U}_{BF}/{U}_{BB}=z+1/2$ , in agreement with the experimental observations. For unpolarized fermionic impurities, the coherence revivals are irrelevant to the strength of the fermion-fermion interactions.The impurity effects on the quantum coherence of a few-boson system are studied within the two-site Hubbard model. Periodical collapses and revivals of coherence occur in the presence of either polarized or unpolarized fermionic impurities. The relative strength ${U}_{BF}/{U}_{BB}$ of the boson-fermion interaction versus the boson-boson interaction plays a key role in the coherence revivals. As the average filling of the impurity increases, the coherence revivals remain nearly unaffected for ${U}_{BF}/{U}_{BB}=z$ ($z\ensuremath{\in}Z$ is an integer) while the odd revival peaks are damped for ${U}_{BF}/{U}_{BB}=z+1/2$, in agreement with the experimental observations. For unpolarized fermionic impurities, the coherence revivals are irrelevant to the strength of the fermion-fermion interactions.

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The coherence of boson–fermion mixed system

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Felipe Mondaini, Thereza Paiva, Raimundo R. dos Santos +1 more

We have considered the half-filled disordered attractive Hubbard model on a square lattice, in which the on-site attraction is switched off on a fraction $f$ of sites, while keeping a finite $U$ on the remaining ones. Through quantum Monte Carlo simulations for several values of $f$ and $U$ and for system sizes ranging from $8\ifmmode\times\else\texttimes\fi{}8$ to $16\ifmmode\times\else\texttimes\fi{}16$, we have calculated the configurational averages of the equal-time pair structure factor ${P}_{s}$ and, for a more restricted set of variables, the helicity modulus ${\ensuremath{\rho}}_{s}$, as functions of temperature. Two finite-size scaling Ans\"atze for ${P}_{s}$ have been used: one for zero temperature and the other for finite temperatures. We have found that the system sustains superconductivity in the ground state up to a critical impurity concentration ${f}_{c}$ , which increases with $U$ , at least up to $U=4$ (in units of the hopping energy). Also, the normalized zero-temperature gap as a function of $f$ shows a maximum near $f\ensuremath{\sim}0.07$ for $2\ensuremath{\lesssim}U\ensuremath{\lesssim}6$. Analyses of the helicity modulus and of the pair structure factor led to the determination of the critical temperature as a function of $f$ for $U=3$ , 4, and 6: they also show maxima near $f\ensuremath{\sim}0.07$, with the highest ${T}_{c}$ increasing with $U$ in this range. We argue that, overall, the observed behavior results from both the breakdown of charge-density-wave-superconductivity degeneracy and the fact that free sites tend to ``push'' electrons toward attractive sites; the latter effect being more drastic at weak couplings.We have considered the half-filled disordered attractive Hubbard model on a square lattice, in which the on-site attraction is switched off on a fraction $f$ of sites, while keeping a finite $U$ on the remaining ones. Through quantum Monte Carlo simulations for several values of $f$ and $U$ and for system sizes ranging from $8\ifmmode\times\else\texttimes\fi{}8$ to $16\ifmmode\times\else\texttimes\fi{}16$, we have calculated the configurational averages of the equal-time pair structure factor ${P}_{s}$ and, for a more restricted set of variables, the helicity modulus ${\ensuremath{\rho}}_{s}$, as functions of temperature. Two finite-size scaling Ans\"atze for ${P}_{s}$ have been used: one for zero temperature and the other for finite temperatures. We have found that the system sustains superconductivity in the ground state up to a critical impurity concentration ${f}_{c}$, which increases with $U$, at least up to $U=4$ (in units of the hopping energy). Also, the normalized zero-temperature gap as a function of $f$ shows a maximum near $f\ensuremath{\sim}0.07$ for $2\ensuremath{\lesssim}U\ensuremath{\lesssim}6$. Analyses of the helicity modulus and of the pair structure factor led to the determination of the critical temperature as a function of $f$ for $U=3$, 4, and 6: they also show maxima near $f\ensuremath{\sim}0.07$, with the highest ${T}_{c}$ increasing with $U$ in this range. We argue that, overall, the observed behavior results from both the breakdown of charge-density-wave-superconductivity degeneracy and the fact that free sites tend to ``push'' electrons toward attractive sites; the latter effect being more drastic at weak couplings.

arXiv:0807.3931Physical Review BNov 19, 200813 citations

U_{BF}/U_{BB}

U_{BF}/U_{BB}=z

(

z\in Z

is an integer) while the odd revival peaks are damped for

U_{BF}/U_{BB}=z+1/2

, in agreement with the experimental observations. For unpolarized fermionic impurities, the coherence revivals are irrelevant to the strength of the fermion-fermion interactions.

{U}_{BF}/{U}_{BB}

of the boson-fermion interaction versus the boson-boson interaction plays a key role in the coherence revivals. As the average filling of the impurity increases, the coherence revivals remain nearly unaffected for

{U}_{BF}/{U}_{BB}=z

($z\ensuremath{\in}Z$ is an integer) while the odd revival peaks are damped for

{U}_{BF}/{U}_{BB}=z+1/2

, in agreement with the experimental observations. For unpolarized fermionic impurities, the coherence revivals are irrelevant to the strength of the fermion-fermion interactions.

We have developed a semi-analytical framework formulated in the canonical fermion representation to investigate strongly correlated electron systems. We consider the U=

\infty

Hubbard model and used the equation of motion method to calculate the fermion self-energy which has two parts: single and two-boson exchange processes. The emergent bosons here are self-generated local charge and spin-density fluctuations which become strongly time-dependent due to extreme correlations. The computed boson spectral density is a diffusive damped mode with a long tail. The electron self-energy at

d=\infty

is computed self-consistently. The corresponding fermionic spectral density displays a pronounced coherence peak at

ω=0

, while its frequency derivative develops a two-peak structure at finite

ω

. The resistivity shows a linear temperature dependence over a broad range, crossing over to coherent Fermi-liquid behavior at extremely low temperatures.

We have considered the half-filled disordered attractive Hubbard model on a square lattice, in which the on-site attraction is switched off on a fraction

f

of sites, while keeping a finite

U

on the remaining ones. Through quantum Monte Carlo simulations for several values of

f

and

U

and for system sizes ranging from $8\ifmmode\times\else\texttimes\fi{}8$ to $16\ifmmode\times\else\texttimes\fi{}16$, we have calculated the configurational averages of the equal-time pair structure factor

{P}_{s}

and, for a more restricted set of variables, the helicity modulus ${\ensuremath{\rho}}_{s}$, as functions of temperature. Two finite-size scaling Ans\"atze for

{P}_{s}

have been used: one for zero temperature and the other for finite temperatures. We have found that the system sustains superconductivity in the ground state up to a critical impurity concentration

{f}_{c}

, which increases with

U

, at least up to

U=4

(in units of the hopping energy). Also, the normalized zero-temperature gap as a function of

f

shows a maximum near $f\ensuremath{\sim}0.07$ for $2\ensuremath{\lesssim}U\ensuremath{\lesssim}6$. Analyses of the helicity modulus and of the pair structure factor led to the determination of the critical temperature as a function of

f

for

U=3

, 4, and 6: they also show maxima near $f\ensuremath{\sim}0.07$, with the highest

{T}_{c}

increasing with

U

in this range. We argue that, overall, the observed behavior results from both the breakdown of charge-density-wave-superconductivity degeneracy and the fact that free sites tend to ``push'' electrons toward attractive sites; the latter effect being more drastic at weak couplings.