Any experimental realization of Bose-Einstein condensation (BEC) deals with composite bosons (cobosons), which are quasi-particles made of fermion pairs that suffer Pauli blocking. We evidence that the prime consequence of the Pauli exclusion principle is to prevent cobosons from having their centers of mass located at the same position within their spatial extension. We moreover predict a many-body effect induced by Pauli blocking that leads to high interference wave modes resulting from fermion exchanges between two colliding coboson condensates. These two effects can be detected by measuring spatial correlation functions. We here propose an original procedure to exactly derive such correlation functions for Frenkel-like cobosons characterized by just their momentum. We physically extend the obtained results to more complex Wannier-like cobosons that have an additional relative motion index. In addition to revealing the physics involved in results previously obtained for elementary boson condensates, we use Shiva diagrams to show how it is changed for cobosons. The predictions we here present, established for matter bosons, are directly applicable to experiments.
Any experimental realization of Bose-Einstein condensation (BEC) deals with composite bosons (cobosons), which are quasi-particles made of fermion pairs that suffer Pauli blocking. We evidence that the prime consequence of the Pauli exclusion principle is to prevent cobosons from having their centers of mass located at the same position within their spatial extension. We moreover predict a many-body effect induced by Pauli blocking that leads to high interference wave modes resulting from fermion exchanges between two colliding coboson condensates. These two effects can be detected by measuring spatial correlation functions. We here propose an original procedure to exactly derive such correlation functions for Frenkel-like cobosons characterized by just their momentum. We physically extend the obtained results to more complex Wannier-like cobosons that have an additional relative motion index. In addition to revealing the physics involved in results previously obtained for elementary boson condensates, we use Shiva diagrams to show how it is changed for cobosons. The predictions we here present, established for matter bosons, are directly applicable to experiments.
We predict the existence of high frequency modes in the interference pattern of two condensates made of fermionic-atom dimers. These modes, which result from fermion exchanges between condensates, constitute a striking signature of the dimer composite nature. From the 2-coboson spatial correlation function, that we derive analytically, and the Shiva diagrams that visualize many-body effects specific to composite bosons, we identify the physical origin of these high frequency modes and determine the conditions to see them experimentally by using bound fermionic-atom pairs trapped on optical lattice sites. The dimer granularity which appears in these modes comes from Pauli blocking that prevents two dimers to be located at the same lattice site.
The quantum nature of elementary bosons can be completely erased by using coherent states known as Glauber states. Here, we consider composite bosons (cobosons) made of two fermions and look for the possibility of erasing the bosonic quantum nature of the field and the fermionic quantum nature of its constituents, when the distribution of the coboson Schmidt decomposition is either flat like Frenkel excitons or localized like Wannier excitons. We show that for Frenkel-like cobosons, complete erasure of the field quantum nature is possible up to a density that is a sizable fraction of the number of fermion-pair states making up the coboson at hand. At a higher density, the Pauli exclusion principle between fermionic constituents shows up dramatically. It induces (i) a decrease in the number-operator eigenvalues down to 1 and an increase in the number-state second-order correlation functions up to 2; (ii) the disappearance of the usual sharp peak in the coherent-state distribution and an increase in the coherent-state second-order correlation function up to 2. It also is possible to construct number states and coherent states for Wannier-like cobosons, but their forms are far more complex. Finally, we show that Pauli blocking makes the coboson coherent states qualitatively different from Anderson's ansatz.
Abstract This book bridges the gap between two major fields in condensed matter physics: semiconductors and superconductors. Through an original perspective that their key particles, excitons and Cooper pairs, are composite bosons (cobosons), the book raises fundamental questions: how does the Pauli exclusion principle affect the fermionic components of bosonic particles at the microscopic level, and how does this appear in the coboson many-body physics at the macroscopic level? What insights would the study of Wannier excitons, Frenkel excitons, and Cooper pairs provide about the “bosonic condensation” of composite bosons and how it differs from the Bose-Einstein condensation of elementary bosons? The book starts from a solid mathematical and physical foundation to derive excitons and Cooper pairs and introduces Shiva diagrams as a graphic support to grasp the many-body physics induced by fermion exchange in the absence of fermion-fermion interaction–a mechanism not visualized in standard Feynman diagrams. The book also covers composite bosons related to excitons: trions, biexcitons, and polaritons. The last part of the book is devoted to composite boson condensation, from the prototypical Bose-Einstein condensation of free elementary bosons and the consequence of interaction, to interacting electrons in the dense regime, to electron-hole pairs in the dense and dilute regimes. Advanced undergraduate and graduate students in physics, with no prior background, will benefit from this book, as numerous appendices provide the materials required to follow the various chapters. The concepts and formalism presented should also prove useful in research on ultracold atomic gases, polariton condensation, and quantum information.
Molecules made of two fermionic atoms are ``cobosons''---a contraction for ``composite bosons.'' These molecules ``feel'' each other not only through interactions between atoms, but also through the Pauli exclusion between their fermionic components. In order to point out the importance of this Pauli exclusion in cold atom physics, we have calculated here the energy change of N identical cobosonic molecules when a similar molecule, made of atoms having possibly different spin states, is added. Due to the difference in the number of fermion exchanges with a molecule having zero, one, or two atoms identical to the ones already present in the system, we may think that this energy change can take three different values, even for spin-independent interatomic interactions. We actually find that the energy change, in the Born approximation, is exactly the same at all orders in density, when the added molecule has two or just one atom identical to the ones already there. In other words, the scattering length is predicted to be the same if the added molecule can have exchanges with one set of fermionic components or with two sets. This unexpected equality, which of course holds for spin-independent interactions only, results from a subtle balance in the fermion exchanges. To prove it, we make use of a recent extension of the composite-exciton many-body theory we have constructed, to any type of cobosons, the physical understanding of the various exchange processes being enlightened by the Shiva diagram representation (so named because of the multiarm structure reminiscent of the Hindu god Shiva) of this many-body theory.
This book bridges a gap between two major communities of Condensed Matter Physics, Semiconductors and Superconductors, that have thrived independently. Through an original perspective that their key particles, excitons and Cooper pairs, are composite bosons, the authors raise fundamental questions of current interest: how does the Pauli exclusion principle wield its power on the fermionic components of bosonic particles at a microscopic level and how this affects the macroscopic physics? What can we learn from Wannier and Frenkel excitons and from Cooper pairs that helps us understand "bosonic condensation" of composite bosons and its difference from Bose-Einstein condensation of elementary bosons? The authors start from solid mathematical and physical foundation to derive excitons and Cooper pairs. They further introduce Shiva diagrams as a graphic support to grasp the many-body physics induced by fermion exchange - a novel mechanism not visualized by standard Feynman diagrams. Advanced undergraduate or graduate students in physics with no prior background will benefit from this book. The developed concepts and methodology should also be useful to present researches on ultracold atomic gases, exciton-polaritons, and quantum information.
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.