My research interest is closely related to the formulation of quantum many-body theory of ultracold trapped bosons. The research activity of my group is focused on the investigations of quantum and statistical properties of weakly interacting Bose gas. Our research activity also involves the applications of our ab initio quantum many-body calculation to study structural properties of atomic clusters and molecules. Our group is also actively engaged in the theoretical study of quantum chaos and thermalization of eigenstates which is very recently experimentally observed in the optical lattice. I did my M.Sc in Physics with Nuclear Physics specialization (1994) and PhD(2000) on development of 3-D supersymmetric quantum mechanics. I did my Postdoc in the field of quantum chaos in HongKong Baptist University and in the field of Bose Einstein condensation in University of Oklahoma. Presently I am collaborating with ICTP, University of Padova (Italy), University of Sao Paulo (Brazil), University of Heidelberg (Germany) and University of South Africa (South Africa). I have published 71 research papers in the peer reviewed International scientific journals (26 in Physical Review) and 6 research papers in National peer-reviewed journals. I have been awarded ICTP (International Center for Theoretical Physics, Trieste, Italy) Regular Associateship for 7 yrs 2015-2021.
B. Sc. ( Lady Brabourne College, 1992)
M. Sc ( Calcutta University, 1994)
PhD (Calcutta University, 2000)
Postdoc on quantum chaos in Hong Kong Baptist University (2001)
Postdoc on Bose Einstein condensation, University of Oklahoma, USA (2003)
I did my PhD on the supersymmetric quantum mechanics in the Calcutta University under the supervision of Prof. Tapan Kumar Das. I obtained the PhD award on 2000 and joined as a postdoctoral research fellow in the Hongkong Baptist University, Hong Kong. I worked there on quantum chaos under the supervision of Prof. Bambi Hu. Next year I moved to University of Oklahoma, Norman and started work on the Bose Einstein condensation in the department of Physics and Astronomy. I worked there with Prof. D. K. Watson. After my return I joined as a Lecturer in a CSC college, Berhampore Krishnath College, Berhampore. In 2006 I moved to Lady Brabourne College and served there as Assistant Professor till middle of 2012. Then I went to Kalyani University and joined the department of Physics as Associate Professor. In December 2013 I moved to the Presidency University.
Present scientific research and future proposal
A) Statistical Relaxation, eigenstate thermalization hypothesis and many-body localization and information entropy.
Transition from localization to delocalized phases in many-body quantum systems due to interparticle interaction has received a great interest in recent days. Nonintegrable quantum systems thermalize and the eigenstate thermalization hypothesis is considered as the underlying mechanism. The standard measure of thermalization in the quench dynamics in many-body system is the study of dynamics of von Neumann entropy. This is the most challenging research area in many-body physics.
We have solved the exact quench dynamics of interacting bosons by utilizing the multiconfiguration time dependent Hartree for bosons (MCTDHB). Apart from Shannon information entropy we also define other measures of many-body information entropies. Our numerical calculation nicely show that for weak interaction the system is in prethermalized state. Whereas very strong interaction pushes the system to thermalization. ETH is also established as the expectation values of typical obsevables saturate to microcanonical value. Our numerical works are able to manifest the recent experimental observation on the transition from prethermalization to thermalization state and the coexistence of prethermalization and thermalization for long range interaction. This work is almost finished and it would be the first theoretical calculation which proves the experimental observation. MCTDHB allows the exact quench dynamics and offers the many-body physics. We also calculate both first-order, second-order and higher-order correlation function which can be obtained in the interference experiment of Bose Einstein condensation. Our numerical results also demonstrate that the statistical relaxation, thermalization and saturation in the dynamics of many-body information entropy are synchronized.
Future Work:
1) We are working for interacting bosons in 1D optical lattice. Utilizing the different filling factor both for commensurate and incommensurate we nicely demonstrate the superfluid to Mott insulator phase transition. We also correlate the delocalization to localization transition in terms of the definition of statistical entropy.
The ETH can be verified by the quench dynamics in entropy for larger interaction. MCTDHB also allows us to study the pathway from condensation to fragmentation to fermionization in term of several measures of entropy. The effect of realistic long range interaction and dynamics of correlation are the important issue in this direction. The full dynamics will facilitate to show how the correlation is gradually build up and then lost when the system makes transition to thermalization for larger interaction.
2) We are trying to establish that ETH can be verified by the observation that all definition of thermodynamics will be universal. The study of interacting bosons in optical lattice and harmonic oscillator trap and the establishment of ETH will be the first theoretical many-body calculation for realistic and experimentally achievable system.
B) Quantum many body formulation and its numerical implementation for ultracold trapped bosons and Bose Einstein condensation (BEC).
Since the experimental achievement of BEC, it is the most challenging research area both for experimental and theoretical physicist as it is highly complex many-body systems. BEC is interesting by itself where the concepts from different branches of physics, condensed matter, statistical physics, quantum mechanics are indeed required for its correct description. It is the system which facilitates the study of quantum effect on macroscopic scale. The presence of external trap makes the system inhomogeneous and exhibits several special features. Due to its uniqueness it puts a challenge to theoretical physicist to provide the theory which can incorporate all essential features. BEC is truly macroscopic but it never reaches thermodynamic limit. So it exhibits finite sized effect and the possibility of phase transition is a long term question since its first discovery. Although the system is dilute, the interatomic interaction plays an important role in the measurement of several properties of the system. The interatomic correlation is also crucial for the attractive BEC. Thus it definitely requires quantum many-body calculation, keeping interatomic correlation and using realistic interatomic interaction.
However till now the Gross Pitaveskii (GP) mean-field theory is the most efficient tool in this field as the number of atoms in the external trap varies from just few to several millions. Although the GP equation qualitatively gives the essential features of BEC, however discripancy remains for quantitative estimate. It uses contact interaction which is not a realistic interatomic interaction and also interatomic correlation is not taken into account. However in present days experiments, utilizing the Feshbach resonance one can truly make strongly interacting BEC. So one indeed needs the many-body calculation. Diffusion Monte Carlo (DMC) is an exact method and can take care of realistic shape-dependent potential. However due to severe computational restriction DMC can treat maximum 100 bosons in the trap. It is admitted that there is no other ab initio exact method even for few-body (N=4) problems. One has to take a proper approximation for the correct description.
Here we propose to decompose the many-body wave function into two-body Faddeev component and keep all possible two-body correlations. Since 2004, we are gradually improving our technique. The basic scenario of our methodology : when two particles interact, the remaining are inert spectators. Thus we deliberately ignore the contribution coming from three-body correlation. This choice is perfectly suitable for the description of experimental BEC. We choose van der Waals interaction and can keep quite large number of bosons. We have extensively applied our methodology ( called Correlated Potential Harmonic Expansion Method (CPHEM) ) for several experimentally achieved BEC and have reproduced the experimental results nicely. Our methodology is applicable for correlated BEC, exhibits finite sized effect, uses realistic interatomic interaction and can tackle the whole range of atom number which are considered experimentally. All static, dynamic and thermodynamic results have been reproduced well. This is the first many-body calculation which accurately reproduce the controlled collapse experiment of JILA.
Future Plan
i) We are trying to extend our methodology to probe the BEC-BCS crossover.
ii) We are working on the strongly correlated dipolar Bose gas which is very special due to its anisotropic nature of interaction. Mean field GP theory can never produce the real experimental features. The utilization of CPHEM will be a good step in this direction.
Iii) The possibility of incorporation of three-body correlation is going on.
C) Theoretical studies of nonlinearity and quantum chaos in BEC: Energy level statistics and spectral fluctuation
It is an well established fact that integrable systems exhibit Poisson statistics and chaotic systems exhibit Wigner statistics in the energy level distribution. From the earlier study of spectral statistics in atomic and nuclear systems, Bohigas conjectured that lowlying levels are uncorrelated and high lying levels are correlated and exhibit a smooth transition from Poission to GOE (Gaussian Orthoginal Ensemble) .
We analyse the spectral statistics, spectral correlation for the energy spectra of interacting trapped bosons. Trapped bosons are not only complex but very interesting for the existence of two energy scale.; the interatomic interaction and the trapping potential. Our observations are as follows :
1) Low-lying levels are of collective nature and highly correlated and the spectral statistics is close to Wigner.
2) This is the first realistic extensive calculation where we observe the breakdown of BGS conjecture.
3) We also observe the existence of Shnirelmn peak in spectral statistics.
4) We have also done all possible spectral analysis of Rb spectra.
5) We analyse the recent experimental results of Er-isotopes and conclude that interacting trapped bosons is a realistic system which shows smooth transition from Wigner to Poisson statistics. The possibuility of chaos has been discussed.
6) For the first time we show that BEC is the experimentally achivable system where we demonstrate that $1/f^{\alpha}$ noise is the ubiquitous in nature.
Future Work :
1) We are extending our calculation for the anharmonic trap which gives additional inhomogenity to the system.
2) Work for truly dipolar BEC is going on.
D) Dynamical instability of (driven) Bose-Einstein condensate and
exploration of suitable control mechanisms.
This is another rich area of study by MCTDHB, where we can consider the driven Bose-Einstein condensation and we can explore suitable mechanism for its dynamical instability. The work in this direction is under process.
Apart from this I also work in different few-body system like van der Waals cluters which exhibit Efimov physics.
Teaching Experience :
Assistant and Sr Assistant Professor : 2000 – 2012
Associate Professor : 2012 – till now
Details of Teaching Experience :
1) Associate Professor position in Presidency University, Calcutta, 26 December 2013 till now.
2) Associate Professor position in Kalyani University, Calcutta, 23 August 2012 till 25 December 2013.
3) Assitant Professor in Lady Brabourne College, Calcutta 1 August 2006 to 22 August 2012.
4) Senior Lecturer Post in Krishnath College 31 March 2000 to 31 July 2006.
Major subject taught
1) Subjects taught in undergraduate courses ( since 2000 till now)
A) UG 1 : Mathematical Physics.
B) UG 2 : Electricity and magnetism.
C) UG 3 : Nuclear Physics and statistical Physics ang UG theses.
2) Subjects taught in Master courses (since 2009 till now)
A) Sem 1 : Mathematical Physics
B) Sem 2 : Atomic and Molecular Physics and Nuclear Physics
C) Sem 3 : Nuclear Physics
D) Sem 4 : Master Theses
Supervised seven completed Ph.D Thesis
1) Anasuya Kundu, Ph. D. University of Calcutta, 2008.
Title : Study of some aspects of Bose-Einstein condensation using realistic interatomic interaction.
2) Anindya Biswas, Ph. D. University of Calcutta, 2011.
Title : Study of many-body effect on the trapped interacting Bose gas.
3) Pankaj Kumar Debnath, Ph. D. University of Calcutta, 2014.
Title: Study of Bose Einstein condensation in anharmonic and deformed trap.
4) Sudip Kumar Haldar, Ph. D. University of Calcutta, 2015. Title: stability of Bose-Einstein condensation in shallow optical traps.
5)Kamalika Roy, JRF Fellow in DAE-BRNS project, working on nonlinearity in BEC. Registered in Calcutta University thesis report received.
6. Sangita Bera, Ph.D. Presidency University, 2020.
Title: Thermodynamics and Statistical Fluctuations for the Trapped Interacting Bose Gas.
7. Rhombik Roy, PhD Presidency University, 2023.
Title : Quantum many-body physics for interacting bosons in optical lattice.
Regular Associate of ICTP, Italy.
PUBLICATION IN 2017-2019 ( 13 in International journals)
(Before 2019 publications are given in full CV)
1) Fidelity and Entropy production in quench dynamics of interacting bosons in an optical lattice. Rhombik Roy, Camille Lévêque, Axel U. J. Lode, Arnaldo Gammal, and Barnali Chakrabarti, Quantum Reports, 1, 304 (2019).
2) Sorting Fermionization from Crystallization in Many-Boson Wave functions S.Bera, B. Chakrabarti, A. Gammal, M. C. Tsatsos, Mantile L. Lekala, B. Chatterjee, C. Lévêque, and A. U. J. Lode, Scientific Reports, 9, 17873 (2019).
3)Probing relaxation dynamics of few strongly correlated bosons in 1D triple well optical lattice, Sangita Bera, Rhombik Roy, Arnaldo Gammal, B.Chakrabarti, Budhaditya Chatterjee, J. Phys B, 52, 21 (2019).
4) Correlation dynamics of dipolar bosons in 1D triple well optical lattice, S. Bera, L. Salasnich and B. Chakrabarti, Symmetry, 11, 909 (2019).
5) Statistical fluctuations and quasi phase transition of mesoscopic Bose Einstein condensation in anharmonic trap, S. Bera, M. L. Lekala, G. J. Rampho, B. Chakrabarti and S. Bhattacharyya, Physics A, 526, 121053 (2019).
6) Information entropy for a two-dimensional rotating Bose-Einstein condensate, K. K. Ramavarmaraja, B. Chakrabarti, A. Gammal, J. Low Temp. Phys., 194, 14 (2019).
7)Phases, many-body entropy measures, and coherence of interacting bosons in optical lattices, R. Roy, A. Gammal, M. C. Tsatsos, B. Chatterjee, B. Chakrabarti, and A. U. J. Lode. Phys. Rev. A, 97, 043625 (2018).
8) Characteristic features of the Shannon information entropy of dipolar Bose-Einstein condensates T.Sriraman, B.Chakrabarti, A. Trombettoni, and P. Muruganandam, J. Chem. Phys. 147, 044304 (2017).
9) Spectral analysis of molecular resonances in Erbium isotopes: Are they close to semi-Poisson? by K. Roy, B. Chakrabarti, N. D. Chavda, V. K. B. Kota, M. L. Lekala and G. J. Rampho, Euro. Phys. Lett. 118, 46003 (2017).
10) Structural and quantum properties of van der Waals cluster near the unitary regime. M. L. Lekala, B. Chakrabarti, S. K. Haldar, R Roy, G. J.Rampho, Phys. Lett. A 381, 2256 (2017).
11) Statistical properties and condensate fluctuation of attractive Bose gas with finite number of particles. S. Bera, M. L. Lekala, B. Chakrabarti, S. Bhattacharyya and G. J. Rampho, Physica A, 481, 79 (2017).
12) Application of conditional shape invariance symmetry to obtain the eigenspectrum. S. Bera , Energy spectrum of the mixed potential V (r) = ar + br^ 2 + r c + l∗(l+1)r^ {2}, B. Chakrabarti and T.K. Das, Phys. Lett. A 381, 1356 (2017).
13) Use of two-body correlated basis functions with van der Waals interaction to study the shape-independent approximation for a large number of trapped interacting bosons. M. L. Lekala, B. Chakrabarti, T. K. Das, G. J. Rampho, S. A. Sofianos, R. M. Adam and S. K. Haldar, J.LowTemp Phys, 187, 232 (2017).
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