# Collective States And The Statistics Of Systems Of Identical Atoms

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### Number-phase-squeezed few-photon state generated from

atoms are in the same pure state, the collective atomic state can be described by a single spin N=2. The con-cept of squeezing in the spin or SU(2) algebra [16,19{26] provides a mathematical de nition of squeezed states in a system of two-level atoms and in other systems that can be described by the spin algebra. Yurke et al. [21]

### Guiding-center dynamics of vortex dipoles in Bose-Einstein

dipoles exhibit essentially identical quasiperiodic behavior. II. EXPERIMENT Our apparatus and experimental procedure are described elsewhere [11,22]. We begin with an oblate 87Rb conden-sate of ∼6 ×105 atoms in the F = 1,m F =−1 state, conﬁned in a time-averaged, orbiting potential (TOP) mag-netic trap [23] with effective frequencies

### PHYSICAL REVIEW X 10, 041053 (2020)

collective excitations [15,35], it is still challenging to measure the rather small contact due to the weak inter-actions between 173Yb atoms. To overcome this obstacle, we develop a new protocol to extract the contact from the column-integrated momentum distribution without using the inverse-Abel transform, which allows a high signal-to-

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### Identical Particles

Identical Particles Until now, most of our focus has been on the quantum mechanical behaviour of individual particles, or problems which can be factorized into independent single-particle systems.1 However, most physical systems of interest involve the interaction of large numbers of particles; electrons in a solid, atoms in a gas, etc.

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strength and the quantum statistics of the particles. I. INTRODUCTION Collective behavior provides an important pathway to-wards the measurement of various physical properties in a multitude of systems. In particular, material prop-erties pertaining to transport often leave an imprint in the collective motion of the system. For example, the

### Incoherentexcitationoffew-levelmultiatom ensembles

Section 3 investigates the photon statistics of the spontaneously emitted photons as function of number of atoms, bath characteristics and orientation of atomic dipoles. The results are summarized in Section 4. 2. Master Equation and itsexact steady statesolution The basic element of our investigation is a sample of N identical non-overlapping

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### arXiv:2104.12934v1 [quant-ph] 27 Apr 2021

respondence is well established for systems with few de-grees of freedom [15], such as billiards, the kicked rotor, and the Dicke model, where the source of chaos is respec-tively the shape of the billiard, the strength of the kicks, and the collective interaction between light and matter. In the case of systems with many interacting particles,

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### The c onnection between collective diffusion in classic

Fig.1 Two identical pictures of atomic arrangement in the vessel. In the case of distinguishability of atoms, they may be numbered, and the physical state illustrated in Fig. (a) differs from that in Fig (b). Both of these states without numbers would be physically indistinguishable.

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number of systems under identical macroscopic conditions, we can nd macroscopic quantities by averaging over an ensemble of states. That this scheme is equivalent to a temporal average is a hypothesis, as it is assumed that the time evolution of the system would lead to all possible states also represented in the ensemble.

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### Theoretical Statistical Physics - Heidelberg University

collective effects and often do not depend much on microscopic details. As you will learn in this course, at the heart of statistical physics is the art of counting, which is for-malized in the concept of a partition sum. The details of how this has to be done in different systems can be quite challenging, and thus it should not come as a surprise

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Einstein is the correct statistics, and I have decided to write a short note on paramagnetism. W. Pauli in a letter to Schrödinger (1925). All electrons in the Universe are identical two physical situations that differ only by interchange of identical particles are indistinguishable! ΨS ΨA, is evenˆ ˆ ˆ is oddˆ A S S A A P P P P α

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the study of collective quantum phenomena. In the years following, the rst degener-ate Fermi gases of 40K [6] and 6Li [7, 8] were achieved. Cooling of fermions to very low temperatures is harder than cooling bosons. In a single-component gas the Pauli principle prevents the s-wave collision between two identical atoms in the same in-ternal state.

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due to the Bose statistics of the individual helium atoms. Helium is found at two isotopic masses, He 4 and He3 with He3 found only to an extent of 1 part in 107 in natural underground helium.(10) The He4 atom contains an even number of fundamental particles and obeys Bose statistics while the He3 atom obeys Fermi-Dirac statistics. Ptre He3

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Dec 04, 2018 in identical internal states with distinct momenta become distinguishable. The resulting strongly interacting system can exhibit exotic topological and pairing behaviors1 4, many of which are yet to be observed in condensed matter systems. Ultracold atomic gases offer a promising pathway for simulating these rich phenomena5 8. Two recent

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cooled atoms @19#. A low threshold microlaser operating near a photonic band edge may exhibit unusual dynamical, spectral, and statistical properties. We will show that such effects are already evident in band-edge collective spontane-ous emission. A preliminary study of band-edge superradi-ance for atoms resonant with the band edge @20# has shown

### Interference of identical particles from entanglement to

states has recently brought collective quantum phenomena of many identical particles into the spotlight. This tutorial introduces the physics of many-boson and many-fermion interference required for the description of current experiments and for the understanding of novel approaches to quantum computing.

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### Collective Switching and Inversion without Fluctuation of Two

We demonstrate population inversion and sub-Poissonian excitation statistics ofN two-level atoms in the context of collective resonance ﬂuorescence. This occurs within photonic band gap and other conﬁned photonic systems that exhibit sharp features in the optical density of states. When the deviation in the photon density of states between

### Physics Today - Search and Discovery October 2003 http://www

In the process, atoms would move away from the governance by Fermi statistics to the rule of Bose statistics. Regal, Jin, Christopher Ticknor, and John Bohn, all of the Boulder group, reported in July that they had formed molecules from atoms in two differing spin states.8 The researchers started with a degenerate 40K

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For a system with quantized energy and two states e1 and e2, the ratio of the probabilities of the two states is given by the Boltzmann potentials, (t is the temperature kBT) If state e2 is the ground state, e2 = 0, and the sum of exponentials is called the partition function Z, and the sum of probabilities equals 1 then, Z = exp(-e2/t) + 1

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dynamics, although systems may change - quasi-statically - between di↵erent equilibrium states. A macroscopic system, however, consists of many microscopic entities, many degrees of freedom, such as moving atoms in a gas or magnetic / electric dipoles in magnets or ferroelectrics.

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tures consist either of identical fermionic atoms in two di erent hyper ne states, or of two di erent atomic species both occupying only a single hyper ne state. In both cases, the number of atoms for each component is allowed to be di er-ent, which leads to a spin imbalance, or spin polarization. Two di erent atomic

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Strongly interacting systems of ultracold atoms : are NOT direct analogues of condensed matter systems These are independent physical systems with their own personalities , physical properties, and theoretical challenges Strongly correlated systems of ultracold atoms should also be useful for applications in quantum information,

### Exploring Big questions on Small scales with ultracoldatoms

not identical to, thermal equilibrium. The ensemble therefore retains some memory beyond the conserved total energy This holds for interacting systems and in the large volume limit. Prethermalization in ultracold atoms, theory: Eckstein et al. (2009);

### Quantum memory for photons: I. Dark state polaritons

vacuum state) to partially map quantum statistics from light to matter. Recently we have proposed a method that combines the enhancementofthe absorptioncrosssectioninmany-atom systems with dissipation-free adiabatic passage techniques [10{12]. It is based on an adiabatic transfer of the quantum state of photons to collective atomic ex-

### Non-Abelian states of matter - University of São Paulo

non-Abelian states of matter, in which the presence of quasiparticles makes the ground state degenerate, and interchanges of identical quasiparticles shift the system between different ground states. Present experimental studies attempt to identify non-Abelian states in systems that manifest the fractional quantum Hall effect.

### 7 x 11 long - Assets

13 Identical particles 438 13.1 Bosons and fermions 438 13.1.1 Symmetry or antisymmetry of the state vector 438 13.1.2 Spin and statistics 441 13.2 The scattering of identical particles 446 13.3 Collective states 448 13.4 Exercises 450 13.5 Further reading 454 14 Atomic physics 455 14.1 Approximation methods 455 14.1.1 Generalities 455

### Superradiance of a subwavelength array of classical nonlinear

Scully and A. A. Svidzinsky, The effect s of the N atom collective Lamb shift on single photon superradiance, Phys. Lett. A 373 (14), 1283 1286 (2009).

### Research Laboratory of Electronics at MIT

number of ultracold potassium-40 atoms in each of three spin states. (a) At first, all atoms are in one of two spin states: = 5/2 or 9/2. (b) After a magnetic field is ramped through a Feshbach resonance, atoms disappear from the two ini- tial states because they are bound into molecules. (c) Following a radio-frequency nals.

### Lecture 20. Semiconductors, phonons

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Bose-Einstein condensation, ultracold atoms, magnetic trapping, optical trapping, quantum statistics, collective excitations, superfluidity, vortices, quantum gases, degenerate Fermi systems, atom-chips, atom interferometry Introduction and overview Bose-Einstein condensation of atoms was achieved in 1995 and had a major impact of atomic physics.