Composite-boson approach toultracold interacting Fermi gases
Ana Majtey

International symposium on Clustering as a Window on the Hierarchical Structure of Quantum Systems(CLUSHIQ2022)
Oct 31 - Nov 3, 2022

Composite-boson approach toultracold interacting Fermi gases
In collaboration with:- P. A. Bouvrie (UGR-Spain)- E. Cuestas (OIST-Japan)- C. Cormick (UNC-Argentina)- I. Roditi (CBPF-Brazil)- E. Rufeil-Fiori (UNC-Argentina)- M. D. Jiménez (UNC-Argentina)- P. Cespedes (UNC-Argentina)- F. Figueiredo (CBPF-Brazil)Is it experimentally possible to generate multiparticle entangledstates by splitting an ultracold interacting Fermi gas?
How strong is the generated entanglement?
Does this entanglement have observable consequences?
Which are the effects of quantum depletion on the phaseestimation of two interfering mBECs?

Outline
Composite boson formalism
Composite-boson approach to molecular BECs
Entanglement between interacting Fermi gases
Effects of Pauli principle on entangled- enhanced
precision measurements

Outline
Composite boson formalism
Composite-boson approach to molecular BECs
Entanglement between interacting Fermi gases
Effects of Pauli principle on entangled- enhanced
precision measurements

Elementary particles are fermions
Take composite particles with even number offermions. Exchange two of these particles, and thewave function must be symmetric.
How can we have Bose-Einstein condensation ifparticles can't really occupy the same state

How can bosons made of fermions condensate?

Towards a rigorous treatment of composite bosons
Composite boson formalism
Combescot , Tanguy, Europhys. Lett. 55, 390 (2001)
fermions
Leggett, Rev. Mod. Phys. 73, 307 (2001)
bosonsLaw, Pays. Rev. A 71, 034306 (2005)
quantum information approach

For a composite particle,“boson-like behaviour” is a state-dependent property

Towards a rigorous treatment of composite bosons

Towards a rigorous treatment of composite bosons

Entanglement and ideal boson behaviour
Law, Pays. Rev. A 71, 034306 (2005)
Chudzicki, Oke, and Wootters, Phys. Rev. Lett. 104, 070402 (2010)

Outline
Composite boson formalism
Composite-boson approach to molecular BECs
Entanglement between interacting Fermi gases
Effects of Pauli principle on entangled- enhanced
precision measurements

Ultracold Fermi gases

Condensation of molecules at T=0

Feshbach molecule

C. Chin, arXiv:cond-mat/0506313.
P. A. Boubrie, M. C. Tichy, and I. Roditi, Phys. Rev. A 95, 023617 (2017)
E. Cuestas, A. P. Majtey, J. Phys. Condens. Matter 33, 255601 (2021)

Feshbach moleculeFeshbach molecule
single-pair ground state
Schmidt decompositionFeshbach molecule

Ansatz for N pairs
Creation coboson operator

Ground state of N composite bosons

Composite-boson approach to molecular BECs
approximates the ground state

Characteristic dimer-dimer scattering
lengthCondensate fractions

What happens in other systems?

Are there sufficient conditions for the validity of thecoboson ansatz?

1. Phys. Rev. A 100, 012309 (2019)
The coboson ansatz also fails for continuous 1D models

2. Phys. Rev. A 105, 013302 (2022)
3. Composite-boson formalism applied to strongly boundfermion pairs in a one-dimensional trap, submitted (2022)

Outline
Composite boson formalism
Composite-boson approach to molecular BECs
Entanglement between interacting Fermi gases
Effects of Pauli principle on entangled- enhanced
precision measurements

Splitting a molecular BEC

Fermion pairs are distributed binomially on the two modes of a perfectbeam splitter, as for ideal bosons or distinguishable particles
Pairs in each mode are correlated due to Pauli principle

Entanglement between mBECS

Fluctuations of single-particle espectral densities

Fluctuations of single-particle espectral densities

Fluctuations of single-particle espectral densities

Fluctuations of single-particle espectral densities

Bell-like nonlocal quantum correlations

Bell-like state when

CHSH inequality

Bell-like nonlocal quantum correlations

Outline
Composite boson formalism
Composite-boson approach to molecular BECs
Entanglement between interacting Fermi gases
Effects of Pauli principle on entangledenhanced precision measurements

Quantum metrology with identical particles

Interferometers with uncorrelated atoms aire limited by the shotnoise
The best possible accuracy is given by the Kramer Rao boundThis limit can be exceeded with entangled atoms (sub-shot-noiseprecision).
This upper limit to the accuracy, the Heisemberg limit

can be achieved using Twin Fock states.

Twin-Fock state of fermions

Two molecular modes 1 and 2 with M=N/2 pairs

Representation of the BEC regime of a interacting Fermi
gas in a double well potential

Dynamics of two fermions in a double well potential
In the strong binding regimen fermions A and B co-tunnel aspairs

A global phase can be obtained in the dynamics by adjusting
the tunneling that couples the wells.

Phase uncertainty Δθ with respect to shot noise Δθsn of a twin Fockinterferometry realized with molecular Bose–Einstein condensates, as afunction of the interference phase θ and for N=4,12, and 36

Summarizing
Bosonic behavior
entanglement
Ansatz of composite bosons that takes into account all exchangeinteractions.
Fermi gases
1-D systems
Generation of entangled molecular condensates.
CHSH inequality violation.
Deviation of bosonic behavior in interference is a consequence ofcondensate fraction loss
Noise in detection favors the Pauli impact which affects the precision
gain.
With efficient detectors, metrological accuracy comparable to atomic
interferometers can be achieved.

Thanks!
anamajtey@unc.edu.ar