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Barnali Chakrabarti

Publications and source records attributed to Barnali Chakrabarti.

36 records · Page 2Linked to original sources

Correlation dynamics of dipolar bosons in 1D triple well optical lattice

The concept of spontaneous symmetry breaking and off-diagonal long-range order (ODLRO) are associated with Bose-Einstein condensation. However, as in the system of reduced dimension the effect of quantum fluctuation is dominating, the concept of ODLRO becomes more interesting, especially for the long-range interaction. In the present manuscript, we study the correlation dynamics triggered by lattice depth quench in a system of three dipolar bosons in a 1D triple-well optical lattice from the first principle using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). Our main motivation is to explore how ODLRO develops and decays with time when the system is brought out-of-equilibrium by a sudden change in the lattice depth. We compare results of dipolar bosons with contact interaction. For forward quench $(V_{f} > V_{i})$, the system exhibits the collapse-revival dynamics in the time evolution of normalized first- and second-order Glauber's correlation function, time evolution of Shannon information entropy both for the contact as well as for the dipolar interaction which is reminiscent of the one observed in Greiner's experiment [Nature, {415}, (2002)]. We define the collapse and revival time ratio as the figure of merit ($τ$) which can uniquely distinguish the timescale of dynamics for dipolar interaction from that of contact interaction. In the reverse quench process $(V_{i} > V_{f})$, for dipolar interaction, the dynamics is complex and the system does not exhibit any definite time scale of evolution, whereas the system with contact interaction exhibits collapse-revival dynamics with a definite time-scale. The long-range repulsive tail in the dipolar interaction inhibits the spreading of correlation across the lattice sites.

cond-mat.quant-gas↗

Quantum dynamics of few dipolar bosons in a double-well potential

We study the few-body dynamics of dipolar bosons in one-dimensional double-wells. Increasing the interaction strength, by investigating one-body observables, we study in the considered few-body systems tunneling oscillations, self-trapping and the regime exhibting an equilibrating behaviour. The corresponding two-body correlation dynamics exhibits a strong interplay between the interatomic correlation due to non-local nature of the repulsion and the inter-well coherence. We also study the link between the correlation dynamics and the occupation of natural orbitals of the one-body density matrix.

cond-mat.quant-gas↗

Spectral analysis of molecular resonances in erbium isotopes: Are they close to semi-Poisson?

We perform a thorough analysis of the spectral statistics of experimental molecular resonances, of bosonic erbium $^{166}$Er and $^{168}$Er isotopes, produced as a function of magnetic field($B$) by Frisch et al. [Nature 507, (2014) 475], utilizing some recently derived surmises which interpolate between Poisson and GOE and without unfolding. Supplementing this with an analysis using unfolded spectrum, it is shown that the resonances are close to semi-Poisson distribution. There is an earlier claim of missing resonances by Molina et al. [Phys. Rev. E 92, (2015) 042906]. These two interpretations can be tested by more precise measurements in future experiments.

cond-mat.stat-mech↗

Characteristic features of the Shannon information entropy of dipolar Bose-Einstein condensates

Calculation of the Shannon information entropy (S) and its connection with the order-disorder transition, and with inter-particle interaction provide a challenging research area in the field of quantum information. Experimental progress with cold trapped atoms has corroborated this interest. In the present work, S is calculated for the Bose-Einstein condensate (BEC) with dominant dipolar interaction for different dipole strengths, trap aspect ratio and number of particles (N). Trapped dipolar bosons in an anisotropic trap provide an example of system where the effective interaction is strongly determined by the trap geometry. The main conlcusion of the present calculation is that the anisotropic trap reduces the number of degrees of freedom, resulting in more ordered configurations. The Landsberg's order parameter exhibits quick saturation with the increase in scattering length in both prolate and oblate traps. We also define the threshold scattering length which makes the system completely disordered. Unlike non-dipolar BEC in a spherical trap, we do not find a universal linear relation between S and ln N, and we, therefore, introduce a general quintic polynomial fit rather well working for a wide range of particle number.

cond-mat.quant-gas↗

Role of conditional shape invariance symmetry property to obtain eigen-spectrum of the generalized polynomial potential with a Coulomb term

A method based on supersymmteric (SUSY) quantum mechanics has been developed by exploiting conditional Shape invariance property for obtaining exact ground state solution of generalized polynomial potential with Coulomb term. Specific cases have been discussed with extensive analytical calculation. How this method can be used to calculate the excited states has also been demonstrated. We have also used a numerical technique (RKGS) and obtained the energy eigenvalues upto second excited state by solving the Schrodinger equation for quartic and sextic polynomial potentials with the Coulomb term and shown that the analytical results provide very good approximations to the numerical results.

quant-ph↗

Application of conditional shape invariance symmetry to obtain the eigen-spectrum of the mixed potential V (r) = ar + br^2 + c/r + l(l+1)/r^2

We show that the conditional shape invariance symmetry can be used as a very powerful tool to calculate the eigenvalues of the mixed potential V (r) = ar + br^2 +c/r + l(l+1)/r^2 for a restricted set of potential parameters. The energy for any state can be obtained algebraically, albeit for a severely restricted set of potential parameters. We also indicate that each member of the hierarchy of Hamiltonians is basically conditionally translational shape invariant. Comparison of analytically obtained results with numerical results is also presented. Our present methodology can be taken as an alternative treatment for the calculation of any higher order excited states of conditionally exactly solvable (CES) potentials.

quant-ph↗

Condensate fraction and critical temperature of interacting Bose gas in anharmonic trap

By using a correlated many body method and using the realistic van der Waals potential we study several statistical measures like the specific heat, transition temperature and the condensate fraction of the interacting Bose gas trapped in an anharmonic potential. As the quadratic plus a quartic confinement makes the trap more tight, the transition temperature increases which makes more favourable condition to achieve Bose-Einstein condensation (BEC) experimentally. BEC in 3D isotropic harmonic potential is also critically studied, the correction to the critical temperature due to finite number of atoms and also the correction due to inter-atomic interaction are calculated by the correlated many-body method. Comparison and discussion with the mean-field results are presented.

cond-mat.quant-gas↗

Level spacing statistics and spectral correlations in the diffuse van der Waals clusters

We present a statistical analysis of eigenenergies and discuss several measures of spectral fluctuations and spectral correlations for the van der Waals clusters of different sizes. We show that the clusters become more and more complex with increase in cluster size. We study nearest-neighbour level spacing distribution $P(s)$, the level number variance $Σ^2(L)$, and the Dyson-Mehta $Δ_3-$statistics for various cluster sizes. For large clusters we find that although the Bohigas-Giannoni-Schmit (BGS) conjecture seems to be valid, it does not exhibit true signatures of quantum chaos. However contrasting conjecture of Berry and Tabor is observed with smaller cluster size. For small number of bosons, we observe the existence of large number of quasi-degenerate states in low-lying excitation which exhibits the Shnirelman peak in $P(s)$ distribution. We also find a narrow region of intermediate spectrum which can be described by semi-Poisson statistics whereas the higher levels are regular and exhibit Poisson statistics. These observations are further supported by the analysis of the distribution of the ratio of consecutive level spacings $P(r)$ which is independent of unfolding procedure and thereby provides a tool for more transparent comparison with experimental findings than $P(s)$. Thus our detail numerical study clearly shows that the van der Waals clusters become more correlated with the increase in cluster size.

quant-ph↗

Correlated many-body calculation to study characteristics of Shannon information entropy for ultracold trapped interacting bosons

A correlated many-body calculation is presented to characterize the Shannon information entropy of trapped interacting bosons. We reformulate the one-body Shannon information entropy in terms of the one-body probability density. The minimum limit of the entropy uncertainty relation (EUR) is approached by making $N$ very small in our numerical work. We examine the effect of correlations in the calculation of information entropy. Comparison with the mean-field result shows that the correlated basis function is indeed required to characterize the important features of the information entropies. We also accurately calculate the point of critical instability of an attractive BEC, which is in close agreement with the experimental value. Next we calculate two-body entropies in position and momentum spaces and study quantum correlations in the attractive BEC.

cond-mat.quant-gas↗

Macroscopic quantum many-body tunneling of attractive Bose-Einstein condensate in anharmonic trap

We study the stability of attractive atomic Bose-Einstein condensate and the macroscopic quantum many-body tunneling (MQT) in the anharmonic trap. We utilize correlated two-body basis function which keeps all possible two-body correlations. The anharmonic parameter ($λ$) is slowly tuned from harmonic to anharmonic. For each choice of $λ$ the many-body equation is solved adiabatically. The use of the van der Waals interaction gives realistic picture which substantially differs from the mean-field results. For weak anharmonicity, we observe that the attractive condensate gains stability with larger number of bosons compared to that in the pure harmonic trap. The transition from resonances to bound states with weak anharmonicity also differs significantly from the earlier study of Moiseyev {\it et.al.}[J. Phys. B: At. Mol. Opt. Phys. {\bf{37}}, L193 (2004)]. We also study the tunneling of the metastable condensate very close to the critical number $N_{cr}$ of collapse and observe that near collapse the MQT is the dominant decay mechanism compared to the two-body and three-body loss rate. We also observe the power law behavior in MQT near the critical point. The results for pure harmonic trap are in agreement with mean-field results. However we fail to retrieve the power law behavior in anharmonic trap although MQT is still the dominant decay mechanism.

cond-mat.quant-gas↗

Dynamical features of Shannon information entropy of bosonic cloud in a tight trap

We calculate Shannon information entropy of trapped interacting bosons in both the position and momentum spaces, $S_r$ and $S_k$ respectively. The total entropy maintains the fuctional form $S=a + b \ln N$ for repulsive bosons. At the noninteracting limit the lower bound of entropic uncertainty relation is also satisfied whereas the diverging behavior of $S_r$ and $S_k$ at the critical point of collapse for attractive condensate accurately calculates the stability factor. Next we study the dynamics of Shannon information entropy with varying interparticle potential. We numerically solve the time-dependent Gross-Pitaevskii equation and study the influence of increasing nonlinearity in the dynamics of entropy uncertainty relation (EUR). We observe that for small nonlinearity the dynamics is regular. With increase in nonlinearity although Shannon entropy shows large variation in amplitude of the oscillation, the EUR is maintained throughout time for all cases and it confirms its generality. We also study the dynamics in a very tight trap when the condensate becomes highly correlated and strongly inhomogeneous. Time evolution of total entropy exhibits aperiodic and fluctuating nature in very tight trap. We also calculate Landsberg's order parameter for various interaction strengths which supports earlier observation that entropy and order are decoupled.

cond-mat.quant-gas↗

Energy level statistics of interacting trapped bosons

It is an well established fact that statistical properties of energy level spectra are the most efficient tool to characterize nonintegrable quantum systems. The study of statistical properties and spectral fluctuation in the interacting many boson systems have developed a new interest in this direction. Specially we are interested in the weakly interacting trapped bosons in the context of Bose-Einstein condensation (BEC) as the energy spectrum shows a transition from the collective to single particle nature with the increase in the number of levels. However this has received less attention as it is believed that the system may exhibit Poisson like fluctuations due to the existence of external harmonic trap. Here we compute numerically the energy levels of the zero-temperature many-boson systems which are weakly interacting through the van der Waals potential and are in the 3D confined harmonic potential. We study the nearest neighbour spacing distribution and the spectral rigidity by unfolding the spectrum. It is found that increase in number of energy levels for repulsive BEC induces a transition from a Wigner like form displaying level repulsion to Poisson distribution for P(s). It does not follow the GOE prediction. For repulsive interaction, the lower levels are correlated and manifest level repulsion. For intermediate levels P (s) shows mixed statistic which clearly signifies the existence of two energy scales: external trap and interatomic interaction. Whereas for very high levels the trapping potential dominates, genarating Poisson distribution. Comparison with mean-field results for lower levels are also presented. For attractive BEC near the critical point we observe the Shrielman like peak near s=0 which signifies the presence of large number of quasi-degenerate states.

cond-mat.quant-gas↗

Supersymmetric isospectral formalism for the calculation of near-zero energy states: application to the very weakly bound ${^4}$He trimer excited state

We propose a novel mathematical approach for the calculation of near-zero energy states by solving potentials which are isospectral with the original one. For any potential, families of strictly isospectral potentials (with very different shape) having desirable and adjustable features are generated by supersymmetric isospectral formalism. The near-zero energy Efimov state in the original potential is effectively trapped in the deep well of the isospectral family and facilitates more accurate calculation of the Efimov state. Application to the first excited state in 4He trimer is presented.

cond-mat.quant-gas↗

Spectral fluctuation and $\frac{1}{f^α}$ noise in the energy level statistics of interacting trapped bosons

It has been recently shown numerically that the transition from integrability to chaos in quantum systems and the corresponding spectral fluctuations are characterized by $\frac{1}{f^α}$ noise with $1\leqα\leq 2$. The system of interacting trapped bosons is inhomogeneous and a complex system. The presence of external harmonic trap makes it more interesting as in the atomic trap the bosons occupy partly degenerate single-particle states. Earlier theoretical and experimental results show that at zero temperature the low-lying levels are of collective nature and high-lying excitations are of single particle nature. We observe that for few bosons, $P(s)$ distribution shows the Shnirelman peak which exhibits a large number of quasi-degenerate states. For large number of bosons the low-lying levels are strongly affected by the interatomic interaction and the corresponding level fluctuation shows a transition to Wigner with increase in particle number. It does not follow GOE (Gaussian Orthogonal Ensemble) Random Matrix predictions. For high-lying levels we observe the uncorrelated Poisson distribution. Thus it may be a very realistic system to prove that $\frac{1}{f^α}$ noise is ubiquitous in nature.

cond-mat.quant-gas↗

Destruction of attractive bosonic cloud due to high spatial coherence in tight trap

We study coherence of a trapped bosonic cloud with attractive finite-range interaction in a tight harmonic trap. One-body density and pair-distribution function in the ground state for different trap sizes are calculated. We also calculate healing length and the correlation length which signify the presence of high spatial coherence in a very tight trap leading to the destruction of the condensate for a fixed particle number. This is in marked variance with the usual collapse of the attractive metastable condensate when N > Ncr . Thus we investigate the critical frequency and critical size of the trap for the existence of attractive Bose-Einstein condensation. The finite-range interaction gives a nonlocal effect in the effective many-body potential, and we observe a high-density stable branch besides the known metastable branch. Moreover, the new branch shows universal behavior even in the very tight trap.

cond-mat.quant-gas↗

Resonance States and Quantum Tunneling of Bose Einstein condensates in a 3D shallow trap

A correlated quantum many-body method is applied to describe resonance states of atomic Bose-Einstein condensates (BEC) in a realistic shallow trap (as opposed to infinite traps commonly used). The realistic van der Waals interaction is adopted as the interatomic interaction. We calculate experimentally measurable decay rates of the lowest quasi-bound state in the shallow trap. The most striking result is the observation of a new metastable branch besides the usual one for attractive BEC in a pure harmonic trap. As the particle number increases the new metastable branch appears, then gradually disappears and finally usual metastable branch (associated with the attractive BEC in a harmonic trap) appears, eventually leading to the collapse of the condensate.

cond-mat.quant-gas↗

Pair-correlation properties and momentum distribution of finite number of interacting trapped bosons in three dimension

We study the ground state pair-correlation properties of a weakly interacting trapped Bose gas in three dimension by using a correlated many-body method. Use of the van der Waals interaction potential and an external trapping potential shows realistic features. We also test the validity of shape-independent approximation in the calculation of correlation properties.

cond-mat.quant-gas↗

Stability of attractive bosonic cloud with van der Waals interaction

We investigate the structure and stability of Bose-Einstein condensate of $^{7}$Li atoms with realistic van der Waals interaction by using the potential harmonic expansion method. Besides the known low-density metastable solution with contact delta function interaction, we find a stable branch at a higher density which corresponds to the formation of an atomic cluster. Comparison with the results of non-local effective interaction is also presented. We analyze the effect of trap size on the transition between the two branches of solutions. We also compute the loss rate of a Bose condensate due to two- and three-body collisions.

cond-mat.quant-gas↗