Bosons Made of Bosons: Condensation of the Whole or Condensation of the Parts?

Composite bosons made of two bosonic constituents exhibit deviations from ideal bosonic behavior due to their substructure. This deviation is reflected by the normalization ratio of the quantum state of $N$ composites. We find a set of saturable, efficiently evaluable bounds for this indicator, which quantifies the bosonic behavior of composites via the entanglement of their constituents. We predict an abrupt transition between ordinary and exaggerated bosonic behavior in a condensate of two-boson composites.Composite bosons made of two bosonic constituents exhibit deviations from ideal bosonic behavior due to their substructure. This deviation is reflected by the normalization ratio of the quantum state of $N$ composites. We find a set of saturable, efficiently evaluable bounds for this indicator, which quantifies the bosonic behavior of composites via the entanglement of their constituents. We predict an abrupt transition between ordinary and exaggerated bosonic behavior in a condensate of two-boson composites.

arXiv:1308.2896Physical Review ADec 20, 201311 citations

Bosonic behavior of entangled fermions

Malte C. Tichy, Peter Alexander Bouvrie, Klaus Mølmer

Two bound, entangled fermions form a composite boson, which can be treated as an elementary boson as long as the Pauli principle does not affect the behavior of many such composite bosons. The departure from ideal bosonic behavior is quantified by the normalization ratio of $N$ -composite-boson states. We derive the two-fermion states that extremize the normalization ratio for a fixed single-fermion purity $P$ , and establish general tight bounds for this indicator. For very small purities, $P<1/{N}^{2}$ , the upper and lower bounds converge, which allows us to quantify accurately the departure from perfectly bosonic behavior, for any state of many composite bosons.Two bound, entangled fermions form a composite boson, which can be treated as an elementary boson as long as the Pauli principle does not affect the behavior of many such composite bosons. The departure from ideal bosonic behavior is quantified by the normalization ratio of $N$-composite-boson states. We derive the two-fermion states that extremize the normalization ratio for a fixed single-fermion purity $P$, and establish general tight bounds for this indicator. For very small purities, $P<1/{N}^{2}$, the upper and lower bounds converge, which allows us to quantify accurately the departure from perfectly bosonic behavior, for any state of many composite bosons.

arXiv:1208.5985Physical Review AOct 15, 201231 citations

How bosonic is a pair of fermions?

Malte C. Tichy, P. Alex, Er Bouvrie +1 more

Abstract Composite particles made of two fermions can be treated as ideal elementary bosons as long as the constituent fermions are sufficiently entangled. In that case, the Pauli principle acting on the parts does not jeopardise the bosonic behaviour of the whole. An indic-ator for bosonic quality is the composite boson normal-isation ratio χN+1/χN of a state of N composites. This quantity is prohibitively complicated to compute exactly for realistic two-fermion wavefunctions and large com-posite numbers N. Here, we provide an efficient char-acterisation in terms of the purity P and the largest eigenvalue λ1 of the reduced single-fermion state. We find the states that extremise χN for given P and λ1, and we provide easily evaluable, saturable upper and lower bounds for the normalisation ratio. Our results strengthen the relationship between the bosonic qual-ity of a composite particle and the entanglement of its constituents. 1Abstract Composite particles made of two fermions can be treated as ideal elementary bosons as long as the constituent fermions are sufficiently entangled. In that case, the Pauli principle acting on the parts does not jeopardise the bosonic behaviour of the whole. An indic-ator for bosonic quality is the composite boson normal-isation ratio χN+1/χN of a state of N composites. This quantity is prohibitively complicated to compute exactly for realistic two-fermion wavefunctions and large com-posite numbers N. Here, we provide an efficient char-acterisation in terms of the purity P and the largest eigenvalue λ1 of the reduced single-fermion state. We find the states that extremise χN for given P and λ1, and we provide easily evaluable, saturable upper and lower bounds for the normalisation ratio. Our results strengthen the relationship between the bosonic qual-ity of a composite particle and the entanglement of its constituents. 1

Jan 1, 201410 citations

Collective Interference of Composite Two-Fermion Bosons

Malte C. Tichy, Peter Alexander Bouvrie, Klaus Mølmer

The composite character of two-fermion bosons manifests itself in the interference of many composites as a deviation from the ideal bosonic behavior. A state of many composite bosons can be represented as a superposition of different numbers of perfect bosons and fermions, which allows us to provide the full Hong-Ou-Mandel-like counting statistics of interfering composites. Our theory quantitatively relates the deviation from the ideal bosonic interference pattern to the entanglement of the fermions within a single composite boson.The composite character of two-fermion bosons manifests itself in the interference of many composites as a deviation from the ideal bosonic behavior. A state of many composite bosons can be represented as a superposition of different numbers of perfect bosons and fermions, which allows us to provide the full Hong-Ou-Mandel-like counting statistics of interfering composites. Our theory quantitatively relates the deviation from the ideal bosonic interference pattern to the entanglement of the fermions within a single composite boson.

arXiv:1209.3610Physical Review LettersDec 28, 201223 citations

Quantum information approach to Bose–Einstein condensation of composite bosons

Su‐Yong Lee, Jayne E. Thompson, Sadegh Raeisi +2 more

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.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.

arXiv:1409.6479New Journal of PhysicsNov 3, 201511 citations

Canonical Ensemble Statistics of Weakly Interacting Composite Boson Condensation: Thermodynamic Properties

Ming‐Tsung Lee

We present a canonical ensemble approach for weakly interacting composite boson systems, which is confined with a finite number of particles. Composite bosons, made of fermion pairs, correlate to each other through the Coulomb interaction associated with the fermion exchange, and are treated perturbatively. We study Bose–Einstein condensation of composite bosons according to the specific heat capacity, the composite-boson distribution function, and the condensate fraction up to the first-order perturbations. As an example, we investigate two-dimensional confined excitons. The study shows that the fermion exchange tends to assist the exciton condensation by raising the temperature. This stabilization of the exciton condensation owing to the fermion exchange is characterized by a small trough in the specific heat capacity profile. As the temperature becomes higher than the transition temperature, the effective Coulomb interaction reduces the thermal fluctuation of excitons, leading to a negative correction to the specific heat capacity in the normal phase. Weakly interacting excitons stay in a more stable thermodynamic state in comparison with ideal exciton gases.We present a canonical ensemble approach for weakly interacting composite boson systems, which is confined with a finite number of particles. Composite bosons, made of fermion pairs, correlate to each other through the Coulomb interaction associated with the fermion exchange, and are treated perturbatively. We study Bose–Einstein condensation of composite bosons according to the specific heat capacity, the composite-boson distribution function, and the condensate fraction up to the first-order perturbations. As an example, we investigate two-dimensional confined excitons. The study shows that the fermion exchange tends to assist the exciton condensation by raising the temperature. This stabilization of the exciton condensation owing to the fermion exchange is characterized by a small trough in the specific heat capacity profile. As the temperature becomes higher than the transition temperature, the effective Coulomb interaction reduces the thermal fluctuation of excitons, leading to a negative correction to the specific heat capacity in the normal phase. Weakly interacting excitons stay in a more stable thermodynamic state in comparison with ideal exciton gases.

Journal of the Physical Society of JapanOct 4, 20130 citations

N

composites. We find a set of saturable, efficiently evaluable bounds for this indicator, which quantifies the bosonic behavior of composites via the entanglement of their constituents. We predict an abrupt transition between ordinary and exaggerated bosonic behavior in a condensate of two-boson composites.

N

-composite-boson states. We derive the two-fermion states that extremize the normalization ratio for a fixed single-fermion purity

P

, and establish general tight bounds for this indicator. For very small purities,

P<1/{N}^{2}

, the upper and lower bounds converge, which allows us to quantify accurately the departure from perfectly bosonic behavior, for any state of many composite bosons.