We develop a coupled-cluster theory for bosonic mixtures of binary species in external traps, providing a promising theoretical approach to demonstrate highly accurately the many-body physics of mixtures of Bose–Einstein condensates. The coupled-cluster wavefunction for the binary species is obtained when an exponential cluster operator eT, where T = T(1) + T(2) + T(12) and T(1) accounts for excitations in species-1, T(2) for excitations in species-2, and T(12) for combined excitations in both species, acts on the ground state configuration prepared by accumulating all bosons in a single orbital for each species. We have explicitly derived the working equations for bosonic mixtures by truncating the cluster operator up to the single and double excitations and using arbitrary sets of orthonormal orbitals for each of the species. Furthermore, the comparatively simplified version of the working equations are formulated using the Fock-like operators. Finally, using an exactly solvable many-body model for bosonic mixtures that exists in the literature allows us to implement and test the performance and accuracy of the coupled-cluster theory for situations with balanced as well as imbalanced boson numbers and for weak to moderately strong intra- and interspecies interaction strengths. The comparison between our computed results using coupled-cluster theory with the respective analytical exact results displays remarkable agreement exhibiting excellent success of the coupled-cluster theory for bosonic mixtures. All in all, the correlation exhaustive coupled-cluster theory shows encouraging results and could be a promising approach in paving the way for high-accuracy modeling of various bosonic mixture systems.
REFERENCES
1.
E.
Timmermans
, “Phase separation of Bose-Einstein condensates
,” Phys. Rev. Lett.
81
, 5718
(1998
).2.
A. R.
Sakhel
, J. L.
DuBois
, and H. R.
Glyde
, “Condensate depletion in two-species Bose gases: A variational quantum Monte Carlo study
,” Phys. Rev. A
77
, 043627
(2008
).3.
S.
Zöllner
, H. D.
Meyer
, and P.
Schmelcher
, “Composite fermionization of one-dimensional Bose-Bose mixtures
,” Phys. Rev. A
78
, 013629
(2008
).4.
M. D.
Girardeau
, “Pairing, off-diagonal long-range order, and quantum phase transition in strongly attracting ultracold Bose gas mixtures in tight waveguides
,” Phys. Rev. Lett.
102
, 245303
(2009
).5.
K.
Anoshkin
, Z.
Wu
, and E.
Zaremba
, “Persistent currents in a bosonic mixture in the ring geometry
,” Phys. Rev. A
88
, 013609
(2013
).6.
D. S.
Petrov
, “Quantum mechanical stabilization of a collapsing Bose-Bose mixture
,” Phys. Rev. Lett.
115
, 155302
(2015
).7.
J.
Chen
, J. M.
Schurer
, and P.
Schmelcher
, “Entanglement induced interactions in binary mixtures
,” Phys. Rev. Lett.
121
, 043401
(2018
).8.
C.
Ticknor
, “Excitations of a trapped two-component Bose-Einstein condensate
,” Phys. Rev. A
88
, 013623
(2013
).9.
E.
Nicklas
, W.
Muessel
, H.
Strobel
, P. G.
Kevrekidis
, and M. K.
Oberthaler
, “Nonlinear dressed states at the miscibility-immiscibility threshold
,” Phys. Rev. A
92
, 053614
(2015
).10.
A.
Kleine
, C.
Kollath
, I. P.
McCulloch
, T.
Giamarchi
, and U.
Schollwöck
, “Spin-charge separation in two-component Bose gases
,” Phys. Rev. A
77
, 013607
(2008
).11.
A.-C.
Lee
, D.
Baillie
, and P. B.
Blakie
, “Stability of a flattened dipolar binary condensate: Emergence of the spin roton
,” Phys. Rev. Res.
4
, 033153
(2022
).12.
X.
Yu
and P. B.
Blakie
, “Propagating ferrodark solitons in a superfluid: Exact solutions and anomalous dynamics
,” Phys. Rev. Lett.
128
, 125301
(2022
).13.
J. C.
Smith
, D.
Baillie
, and P. B.
Blakie
, “Quantum droplet states of a binary magnetic gas
,” Phys. Rev. Lett.
126
, 025302
(2021
).14.
D. S.
Hall
, M. R.
Matthews
, C. E.
Wieman
, and E. A.
Cornell
, “Measurements of relative phase in two-component Bose-Einstein condensates
,” Phys. Rev. Lett.
81
, 1543
(1998
).15.
D. M.
Stamper-Kurn
, M. R.
Andrews
, A. P.
Chikkatur
, S.
Inouye
, H.-J.
Miesner
, J.
Stenger
, and W.
Ketterle
, “Optical confinement of a Bose-Einstein condensate
,” Phys. Rev. Lett.
80
, 2027
(1998
).16.
S. T.
Chui
, V. N.
Ryzhov
, and E. E.
Tareyeva
, “Vortex states in a binary mixture of Bose-Einstein condensates
,” Phys. Rev. A
63
, 023605
(2001
).17.
G.
Thalhammer
, G.
Barontini
, L.
De Sarlo
, J.
Catani
, F.
Minardi
, and M.
Inguscio
, “Double species Bose-Einstein condensate with tunable interspecies interactions
,” Phys. Rev. Lett.
100
, 210402
(2008
).18.
S.
Gautam
and D.
Angom
, “Rayleigh-Taylor instability in binary condensates
,” Phys. Rev. A
81
, 053616
(2010
).19.
D. J.
McCarron
, H. W.
Cho
, D. L.
Jenkin
, M. P.
Köppinger
, and S. L.
Cornish
, “Dual-species Bose-Einstein condensate of 87Rb and 133Cs
,” Phys. Rev. A
84
, 011603
(2011
).20.
L.
Wacker
, N. B.
Jørgensen
, D.
Birkmose
, R.
Horchani
, W.
Ertmer
, C.
Klempt
, N.
Winter
, J.
Sherson
, and J. J.
Arlt
, “Tunable dual-species Bose-Einstein condensates of 39K and 87Rb
,” Phys. Rev. A
92
, 053602
(2015
).21.
A.
Bhowmik
, P. K.
Mondal
, S.
Majumder
, and B.
Deb
, “Density profiles of two-component Bose–Einstein condensates interacting with a Laguerre–Gaussian beam
,” J. Phys. B: At., Mol. Opt. Phys.
51
, 135003
(2018
).22.
A.
Trautmann
, P.
Ilzhöfer
, G.
Durastante
, C.
Politi
, M.
Sohmen
, M. J.
Mark
, and F.
Ferlaino
, “Dipolar quantum mixtures of erbium and dysprosium atoms
,” Phys. Rev. Lett.
121
, 213601
(2018
).23.
R.
Bai
, D.
Gaur
, H.
Sable
, S.
Bandyopadhyay
, K.
Suthar
, and D.
Angom
, “Segregated quantum phases of dipolar bosonic mixtures in two-dimensional optical lattices
,” Phys. Rev. A
102
, 043309
(2020
).24.
O. E.
Alon
, “Solvable model of a generic driven mixture of trapped Bose–Einstein condensates and properties of a many-boson floquet state at the limit of an infinite number of particles
,” Entropy
22
, 1342
(2020
).25.
R. N.
Bisset
, L. P.
Ardila
, and L.
Santos
, “Quantum droplets of dipolar mixtures
,” Phys. Rev. Lett.
126
, 025301
(2021
).26.
O. E.
Alon
, “Solvable model of a generic trapped mixture of interacting bosons: Reduced density matrices and proof of Bose–Einstein condensation
,” J. Phys. A: Math. Theor.
50
, 295002
(2017
).27.
K.
Dželalija
, V.
Cikojević
, J.
Boronat
, and L.
Vranješ Markić
, “Trapped Bose-Bose mixtures at finite temperature: A quantum Monte Carlo approach
,” Phys. Rev. A
102
, 063304
(2020
).28.
V.
Cikojević
, L. V.
Markić
, and J.
Boronat
, “Harmonically trapped Bose–Bose mixtures: A quantum Monte Carlo study
,” New J. Phys.
20
, 085002
(2018
).29.
M.
Lewenstein
, A.
Sanpera
, and V.
Ahufinger
, Ultracold Atoms in Optical Lattices: Simulating Quantum Many-Body Systems
(Oxford University Press
, Oxford, UK
, 2012
).30.
I.
Morera
, G. E.
Astrakharchik
, A.
Polls
, and B.
Juliá-Díaz
, “Quantum droplets of bosonic mixtures in a one-dimensional optical lattice
,” Phys. Rev. Res.
2
, 022008(R)
(2020
).31.
C.
Lévêque
and L. B.
Madsen
, “Multispecies time-dependent restricted-active-space self-consistent-field theory for ultracold atomic and molecular gases
,” J. Phys. B: At., Mol. Opt. Phys.
51
, 155302
(2018
).32.
O. E.
Alon
, A. I.
Streltsov
, and L. S.
Cederbaum
, “Multiconfigurational time-dependent Hartree method for mixtures consisting of two types of identical particles
,” Phys. Rev. A
76
, 062501
(2007
).33.
L.
Cao
, S.
Krönke
, O.
Vendrell
, and P.
Schmelcher
, “The multi-layer multi-configuration time-dependent Hartree method for bosons: Theory, implementation, and applications
,” J. Chem. Phys.
139
, 134103
(2013
).34.
L.
Cao
, V.
Bolsinger
, S. I.
Mistakidis
, G. M.
Koutentakis
, S.
Krönke
, J. M.
Schurer
, and P.
Schmelcher
, “A unified ab initio approach to the correlated quantum dynamics of ultracold fermionic and bosonic mixtures
,” J. Chem. Phys.
147
, 044106
(2017
).35.
U.
Manthe
and T.
Weike
, “On the multi-layer multi-configurational time-dependent Hartree approach for bosons and fermions
,” J. Chem. Phys.
146
, 064117
(2017
).36.
J.
Paldus
and J.
Čížek
, “Time-independent diagrammatic approach to perturbation theory of fermion systems
,” Adv. Quantum Chem.
9
, 105
(1975
).37.
J.
Čížek
, “On the correlation problem in atomic and molecular systems. Calculation of wavefunction components in Ursell-type expansion using quantum-field theoretical methods
,” J. Chem. Phys.
45
, 4256
(1966
).38.
I.
Lindgren
and J.
Morrison
, in Atomic Many-Body Theory
,
(3rd ed.)
, edited by G. E.
Lambropoulos
and H.
Walther
(Springer; John Wiley & Sons
, Berlin; Chichester, UK
, 2000
), Vol. 3
.39.
R. J.
Bartlett
and M.
Musiał
, “Coupled-cluster theory in quantum chemistry
,” Rev. Mod. Phys.
79
, 291
(2007
).40.
R. F.
Bishop
, U.
Kaldor
, H.
Kümmel
, and D.
Mukherjee
, The Coupled Cluster Approach to Quantum Many-Particle Systems
(Springer
, Heidelberg
, 2003
).41.
Recent Progress in Coupled Cluster Methods: Theory and Applications
, edited by P. C.
Josef
and P.
Pittner
(Springer
, New York
, 2010
).42.
A. F.
White
and G. K. L.
Chan
, “A time-dependent formulation of coupled-cluster theory for many-fermion systems at finite temperature
,” J. Chem. Theory Comput.
14
, 5690
(2018
).43.
H. S.
Nataraj
, B. K.
Sahoo
, B. P.
Das
, and D.
Mukherjee
, “Intrinsic electric dipole moments of paramagnetic atoms: Rubidium and cesium
,” Phys. Rev. Lett.
101
, 033002
(2008
).44.
A.
Bhowmik
, N. N.
Dutta
, and S.
Majumder
, “Vector polarizability of an atomic state induced by a linearly polarized vortex beam: External control of magic, tune-out wavelengths, and heteronuclear spin oscillations
,” Phys. Rev. A
102
, 063116
(2020
).45.
A.
Chakraborty
, S. K.
Rithvik
, and B. K.
Sahoo
, “Relativistic normal coupled-cluster theory analysis of second- and third-order electric polarizabilities of Zn I
,” Phys. Rev. A
105
, 062815
(2022
).46.
A.
Bhowmik
, S.
Roy
, N. N.
Dutta
, and S.
Majumder
, “Study of coupled-cluster correlations on electromagnetic transitions and hyperfine structure constants of W VI
,” J. Phys. B: At., Mol. Opt. Phys.
50
, 125005
(2017
).47.
L. S.
Cederbaum
, O. E.
Alon
, and A. I.
Streltsov
, “Coupled-cluster theory for systems of bosons in external traps
,” Phys. Rev. A
73
, 043609
(2006
).48.
A. F.
White
, Y.
Gao
, A. J.
Minnich
, and G. K. L.
Chan
, “A coupled cluster framework for electrons and phonons
,” J. Chem. Phys.
153
, 224112
(2020
).49.
U.
Mordovina
, C.
Bungey
, H.
Appel
, P. J.
Knowles
, A.
Rubio
, and F. R.
Manby
, “Polaritonic coupled-cluster theory
,” Phys. Rev. Res.
2
, 023262
(2020
).50.
T. S.
Haugland
, E.
Ronca
, E. F.
Kjønstad
, A.
Rubio
, and H.
Koch
, “Coupled cluster theory for molecular polaritons: Changing ground and excited states
,” Phys. Rev. X
10
, 041043
(2020
).51.
B. H.
Ellis
, S.
Aggarwal
, and A.
Chakraborty
, “Development of the multicomponent coupled-cluster theory for investigation of multiexcitonic interactions
,” J. Chem. Theory Comput.
12
, 188
(2016
).52.
L. S.
Cederbaum
and A. I.
Streltsov
, “Best mean-field for condensates
,” Phys. Lett. A
318
, 564
(2003
).53.
O. E.
Alon
, A. I.
Streltsov
, and L. S.
Cederbaum
, “Demixing of bosonic mixtures in optical lattices from macroscopic to microscopic scales
,” Phys. Rev. Lett.
97
, 230403
(2006
).54.
A. U. J.
Lode
, K.
Sakmann
, O. E.
Alon
, L. S.
Cederbaum
, and A. I.
Streltsov
, “Numerically exact quantum dynamics of bosons with time-dependent interactions of harmonic type
,” Phys. Rev. A
86
, 063606
(2012
).55.
E.
Fasshauer
and A. U. J.
Lode
, “Multiconfigurational time-dependent Hartree method for fermions: Implementation, exactness, and few-fermion tunneling to open space
,” Phys. Rev. A
93
, 033635
(2016
).56.
A. U. J.
Lode
, C.
Lévêque
, L. B.
Madsen
, A. I.
Streltsov
, and O. E.
Alon
, “Colloquium: Multiconfigurational time-dependent Hartree approaches for indistinguishable particles
,” Rev. Mod. Phys.
92
, 011001
(2020
).57.
S.
Klaiman
, A. I.
Streltsov
, and O. E.
Alon
, “Solvable model of a trapped mixture of Bose–Einstein condensates
,” Chem. Phys.
482
, 362
(2017
).58.
P. A.
Bouvrie
, A. P.
Majtey
, M. C.
Tichy
, J. S.
Dehesa
, and A. R.
Plastino
, “Entanglement and the Born-Oppenheimer approximation in an exactly solvable quantum many-body system
,” Eur. Phys. J. D
68
, 346
(2014
).59.
O. E.
Alon
and L. S.
Cederbaum
, “Effects beyond center-of-mass separability in a trapped bosonic mixture: Exact results
,” J. Phys.: Conf. Ser.
2249
, 012011
(2022
).60.
T.
Haugset
and H.
Haugerud
, “Exact diagonalization of the Hamiltonian for trapped interacting bosons in lower dimensions
,” Phys. Rev. A
57
, 3809
(1998
).61.
D. A.
Matthews
, “Accelerating the convergence of higher-order coupled-cluster methods II: Coupled-cluster Λ equations and dynamic damping
,” Mol. Phys.
118
, e1757774
(2020
).62.
C.
Huber
and T.
Klamroth
, “Explicitly time-dependent coupled cluster singles doubles calculations of laser-driven many-electron dynamics
,” J. Chem. Phys.
134
, 054113
(2011
).63.
B.
Sverdrup Ofstad
, E.
Aurbakken
, Ø.
Sigmundson Schøyen
, H. E.
Kristiansen
, S.
Kvaal
, and T. B.
Pedersen
, “Time-dependent coupled-cluster theory
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
13
, e1666
(2023
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
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