Particles made of two fermions can in many cases be treated as elementary bosons, but the conditions for this treatment to be valid are nontrivial. The so-called ``coboson formalism'' is a powerful tool to tackle compositeness effects relevant for instance for exciton physics and ultracold atomic dimers. A key element of this theory is an ansatz for the ground state of
N pairs, built from the single-pair ground state combined with the exclusion principle. We show that this ansatz can fail in one-dimensional systems which fulfill the conditions expected to make the ansatz valid. Nevertheless, we also explain how coboson theory can recover the correct ground state. Thus, our work highlights limitations and strengths of the formalism and leads to a better treatment of composite bosons.
We consider composite bosons (cobosons) comprised two elementary particles, fermions or bosons, in an entangled state. First, we show that the effective number of cobosons implies the level of correlation between the two constituent particles. For the maximum level of correlation, the effective number of cobosons is the same as the total number of cobosons, which can exhibit the original Bose–Einstein condensation (BEC). In this context, we study a model of BEC for indistinguishable cobosons with a controllable parameter, i.e., entanglement between the two constituent particles. We find that bi-fermions behave in a predictable way, i.e., the effective number of the ground state coboson is an increasing function of entanglement between a pair of constituent fermions. Interestingly, bi-bosons exhibit the opposite behavior—the effective number of the ground state coboson is a decreasing function of entanglement between a pair of constituent bosons.
Ultracold atomic systems provide a versatile platform for exploring quantum phenomena, offering tunable interactions and diverse trapping geometries. In this study, we investigate a one-dimensional system of trapped fermionic atoms using the composite boson formalism, which describes pairs of opposite-spin fermions as cobosons (short for composite bosons). We solve the Schr\"odinger equation for a $2\ensuremath{\uparrow}+2\ensuremath{\downarrow}$ fermionic system across a broad range of attractive and repulsive interactions by constructing the system's wave function as a superposition of two-coboson states. We determine key observables such as particle density profiles and two-body correlations. The density profiles calculated agree with both the Tonks-Girardeau and Lieb-Liniger limits and provide a portrait of the transition between those regimes. In the strong repulsive regime, the ansatz captures the Fridel-Wigner transition characterized by a doubling of the peaks in the density profiles. Additionally, we compute the low-lying energy spectrum and estimate the pairing gap. Our results highlight the usefulness of the coboson superposition ansatz for exploring quantum phenomena in strongly correlated few-body systems.
Many useful properties of dilute Bose gases at ultra-low temperature are predicted precisely by the product-state ansatz, in which all particles are in the same quantum state. As particle-particle correlations become important, however, the product ansatz begins to fail. We consider a new set of states, which constitute a natural generalization of the product ansatz; the particle-correlated state of
N=l×n identical particles is derived by symmetrizing the
n-fold product of an
l-particle quantum state. The particle-correlated states can be simulated efficiently for large
N, because their parameter spaces, which depend on
l, do not grow with
n. Here we pay special attention to the pure-state case for
l=2, where the many-body state is constructed from a two-particle pure state. These paired wave functions for bosons, which we call pair-correlated states (PCS), were introduced by Leggett [Rev. Mod. Phys.
73, 307 (2001)] as a particle-number-conserving version of the Bogoliubov approximation. We present an iterative algorithm that solves the reduced (marginal) density matrices (RDMs)---these are the correlation functions---associated with PCS in time
O(N). The RDMs can also be derived from the normalization factor of PCS, which is derived analytically in the large
N limit. To test the efficacy of our theory, we analyze the ground state of the two-site Bose-Hubbard model by minimizing the energy of the PCS state, both in its exact form and in its large-
N approximate form. The relative errors of the ground state energy for both cases are within
10−5 for
N=1000 particles over the entire parameter region from a single condensate to a Mott insulator. Moreover, we present numerical results that suggest that PCS might be useful for describing the dynamics in the strongly interacting regime.
On the role of entanglement in the formation and stability of composite bosons by mgr.Zakarya Lasmar Composite bosons are many-body systems made of many elementary bosons, or an even number of elementary fermions.Recently, it was suggested that quantum entanglement can be understood as the origin of the bosonic character of the simplest systems of this type (bipartite composite bosons).This idea motivated a new direction of research: quantum information oriented study of composite particles.In the present work, the role of entanglement in the formation and dynamics of composite bosons is studied.We show that, in some special situations, two entangled fermions can exhibit bosonic behaviour while being specially separated.We propose a nonlocal scheme that leads two pairs of entangled fermions to form an analogue of a two-partite bosonic Fock state.Also, we show that in some situations entanglement can provide stability for a composite particle.In this case, the interaction-free dynamics of an entangled bipartite system appear to mimic the behaviour of two interacting particles.In addition, we discuss the possible reasons that can limit the influence of entanglement on the behaviour of composite particles.The no-signalling condition seems to play a crucial role, which suggests that interactions in some situations become necessary.Regarding the formation of composite bosons, I present an entanglement-based method to study the bosonic quality of fermionic multipartite systems.Using this method, I examine the bosonic quality of the ground state of the extended one-dimensional Hubbard model while tuning the strength of interactions.vii
We assess whether a confined Wigner molecule constituted by
2N fermions behaves as
N bosons or
2N fermions. Following the work by Law [Phys. Rev. A 71, 034306 (2005)] and Chudzicki et al. [Phys. Rev. Lett. 104, 070402 (2010)] we discuss the physical meaning and the reason why a large amount of entanglement is needed in order to ensure a bosonic composite behavior. By applying a composite boson ansatz, we found that a Wigner molecule confined in a two-dimensional trap presents a bosonic behavior induced by symmetry. The two-particle Wigner molecule ground state required by the composite boson ansatz was obtained within the harmonic approximation in the strong interacting regime. Our approach allows us to address few-particle states (widely studied within a variety of theoretical and numerical techniques) as well as a large number of particles (difficult to address due to computational costs). For a large number of particles, we found strong fermionic correlations exposed by the suppression of particle fluctuations. For a small number of particles, we show that the wave function calculated within the composite boson ansatz captures the Friedel-Wigner transition. The latter is shown in a regime in which strong correlations due to the Pauli exclusion principle arise; therefore, we conclude that the coboson ansatz reproduces the many-particle physics of a confined Wigner molecule, even in the presence of strong deviations of the ideal bosonic behavior due to fermionic correlations.