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Questions tagged [bose-einstein-condensate]

A Bose–Einstein condensate is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero. In this state, a large fraction of the bosons occupy the *lowest quantum state* so that macroscopic quantum phenomena are in evidence. Use for all related BEC processes.

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Bose-Einstein condensation of interacting bosons

Consider a bosonic Hamiltonian with two-body interactions $$H=\sum_{ij}T_{ij\,}b_i^\dagger b_j+\frac{1}{2}\sum_{ij}U_{ij\,}b_i^\dagger b_j^\dagger b_j b_i,$$ assuming $U_{ij}=U_{ji}$. Suppose the ...
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Which is the difference between Josephson and Rabi oscillations?

Consider a bosonic Josephson junction, such as a Bose-Einstein condensate trapped in a double-well potential. What are Josephson oscillations and what are Rabi oscillations? In what do they differ?
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Hartree-Fock factorization

I am studying c-field methods applied to Bose-Einstein condensates to understand how one gets to e.g. the dissipative GPE. To do so, one splits the field operator for the Bose gas into a low- and a ...
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In a Bose-Einstein condensate, do the cooled particles lose weight? [closed]

If the elementary particles are cooled, they lose a weight?
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Heisenberg uncertainty principle on bosons at absolute zero [duplicate]

Bosons obey Heisenberg's uncertainty principle but not Pauli's exclusion principle. In Bose-Einstein Condensation quantum effects are much more important and here we get a large number of particles ...
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Why the ground state energy of bosons are 0 at T=0K ? Does it violate Heisenberg's Uncertainity Principle at 0K?

Bosons obey Heisenberg's Uncertainity Principle but do not Pauli's Exclusion Principle. That's why in Bose Condensation we get a large amount of particles in a single state i.e. ground state at T=0K. ...
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“Printing” 3D structures using an atom laser?

An atom laser is a coherent beam of atoms, similar to a laser. This is formed through use of Bose-Einstein condensate. Could such a beam be focused and used to deposit atoms on a surface to build up ...
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Free parameter in Bose Einstein Condensate

In Kapusta and Gale's Finite-Temperature Field Theory book, BEC is derived for a complex scalar by Fourier expanding $$\phi _1 = \sqrt2 \zeta \cos \theta + \sqrt{\frac{\beta}{V}}\sum_{n,\bar p}e^{i(\...
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Bose-Einstein condensation: Bogoliubov Approximation

I'm trying to understand the Bogoliubov approximation from "Statistical Mechanics" by Pathria and Beale. First of all they say Since $a_0^{\dagger}a_0=n_0=O(N)$ and $(a_0a_0^{\dagger}-a_0^{\dagger}...
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Is it possible to use Bose-Einstein condensate for propulsion with today's tech?

Can one use the Bose Einstein condensate which we can produce today for space propulsion, as many theoretical concepts need negative mass and that is a property of Bose Einstein condensate, how ...
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Are Cooper pairs (of electrons) entangled?

I have read this question: Does a normal torch emit entangled photons? where Quantum Journalist says: Although all the particles of a BEC are in a single quantum state, they are not ...
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Bose–Einstein Condensation in one dimensional harmonic oscillator [duplicate]

I was given that there is Bose gas with spin 0 in one harmonic oscillator so the energy levels are: $\epsilon_{n}=\hbar\omega n$ Can this gas go through Bose Einstein Condensation? I think yes, ...
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Observation of Bose-Einstein Condensation

Why it took us so long to see a Bose-Einstein Condensation? Was it because we didn't have the experimental setup or something else?
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How is it possible a quadratic Hermitian Hamiltonian $H = b^\dagger b^\dagger + b b$, with $b$ boson, cannot be diagonalized?

How can a Hermitian Hamiltonian $H = b^\dagger b^\dagger + b b$, with $b$ boson, cannot be diagonlized? Given a Hamiltonian $$\hat H = b^\dagger b^\dagger + b b \tag{1}$$ with $b, b^\dagger$ boson ...
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What happens to the scattering cross section of two fermions with different spins at low temperature?

The scattering cross section for two identical fermions at low temperature is given by: $\sim 8\pi a_1^2(ka_1)^4$. I was wondering what happens if the two fermions have different spins - does it ...
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Chemical potential of a BEC

I know that the chemical potential of a BEC can be calculated with $\mu=\frac{\partial E}{\partial N}$, where $E$ is the energy and $N$ is the number of particles. For the Gross-Pitaevskii equation ...
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How to calculate a one-body reduced density matrix

I calculated eigenvalues and eigenvectors of a many-body problem for a SBEC (spinorial Bose-Einstein Condensate) in the SMA approximation . Then I can calculate the density matrix of this problem. ...
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Creating micro black holes with “bosers”; easier than creating kugelblitzes? [closed]

A "boser" is a coherent matter beam or pulse of Bose-Einstein condensate (and a spin of the word "laser"), sometimes portrayed in science fiction but maybe becoming more a reality. A kugelblitz black ...
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Bosons in Bohmian mechanics

I would like to know if even bosons in the same quantum state, like in a BEC, can be discerned (by their positions) in Bohm's mechanics.
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Intuition behind Bose-Einstein Condensate [closed]

I am trying to learn about Bose–Einstein (BE) condensate, and in doing so I encountered some bizarre phenomena, which is a norm in quantum mechanics. I realized matter would turn into 'waves' and lose ...
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Bose Einstein Condensation

We all know that the Bose Einstein distribution formula is $n=g_i/(e^{α+βi}-1).$ Where alpha is the derivative of constant number of particles that is supposed to be zero. But while studding Bose ...
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Calculate the matrix size for ground states BEC using difference with Gross–Pitaevskii equation

The Ground states BEC at $0$ temperature can be described by Gross–Pitaevskii equation as $(-\frac{\hbar^2}{2m}\nabla^2+V(r)+g|\psi|^2)\psi(r)=\mu\psi(r)$ We limit the BEC in 2D where $V(r)=\frac{1}{...
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Different between droplet and a soliton

I am working on the droplet state in a Bose-Bose mixture. I have a question about the difference between the droplet liquid state and the soliton state: How we can treat a droplet state? And how do we ...
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Mean energy of bosons gas

I am currently doing a question with regards to bosons gases and come across a sticking point. The question is as follows. For a gas of bosons at temperature $T$ below the Bose-Einstein ...
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Expanding the interaction term in Hamiltonian for weakly interacting Bose gas

Let the second quantization Hamiltonian and the Bogoliubov prescription Could you explain me how to obtain the following expression I know that the second term in this expression is equivalent to ...
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JILA Rubidium-87 Bose Einstein condensate

Why was the observation of Bose-Einstein condensation by JILA considered so special? I was under the impression that they were not nearly the first group to observe it, since it was observed with ...
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What's “bimodal” about BEC velocity distributions?

I was just reviewing some papers discussing Bose-einstein condensation, specifically "Creation of a Bose-condensed gas of 87Rb by laser cooling" by Hu et al., and I saw repeated references to the ...
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Macroscopic population of excited states for Bose-Einstein condensation?

I am currently learning about Bose-Einstein condensation (BEC). I understand that the ground state is rapidly populated when the temperature goes below the critical temperature. This macroscopic ...
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Physical interpretation of Bogolyubov sound with zero momentum in BEC

The point with zero momentum in the spectrum of acoustic phonon corresponds to a translation of the crystal. Is there an interpretation like this of the Bogolyubov sound in BEC? I have read that in ...
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Why is the density of a BEC so low?

I've just begun reading C. Pethick and H. Smith's textbook "Bose-Einstein condensation in dilute gases" (Cam. Uni. Press). In the Introduction, they contrast the density of atoms at the centre of a ...
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Bose-Einstein Condensate bonding

How would a material bond with a BEC? Would it have valence electrons? If you were to have a couple hundred atoms in BEC, would they bond with a couple hundred other atoms, a lower amount that how ...
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Is it BEC-BCS crossover the natural framework to explain superconductivity from ultracold atoms?

I know that superfluidity and superconductivity have very distinct characteristics and have specific theories. However, it seems that in ultra-cold atomic gases these phenomena can be understood by a ...
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Phase change into Bose-Einstein Condensate

I am a high school chemistry/physics teacher and I was just wondering what the phase change into/out of a Bose-Einstein Condensate is called? Thanks!
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Why we can't write low energy effective field theory for a gapless system?

Assume that we have an Hamiltonian $$H=H_0+H_{int}$$ where $H_0$ has gappless excitations and $H_{int}$ has usual two body interactions. If $H_0$ were gapped I would able to get low energy effective ...
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Heating A Condensate

There is so much literature out there on Bose Condensates, that it is literally all about the cooling of a gas. But I am interested in the physics of the condensate heating up - can someone explain ...
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Where is the gauge symmetry in an ideal Bose gas?

It seems in the literature that there is a certain notion of a “macroscopic wavefunction” associated with a Bose-Einstein system (see this PSE answer) which exhibits a global $U(1)$-phase symmetry. ...
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Do macroscopic bodies also show quantum nature at extremely low temperatures?

If we consider atoms or molecules and cool them to extremely low tempertures, will they also show quantum nature. Will their wave nature also get dominated? And if they are bosons, will they become a ...
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How to write a wave-fuction of bose einstein condesate bosons in second quantization representation?

Can we write wave function of bose einstein condensation like this $|\psi \rangle=\frac{{c^{\dagger}}^N}{ \sqrt{N!}} |0\rangle$. Or it will be different?
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super bunching effect of bosons

Let say we consider a $N$ pair of elementry bosons (i.e $N$ composite bosons). At very low temperature these bosons will condense into the ground state. If we find the mean occupation number $\langle ...
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Bose Condensation; interacting vs. non-interacting

I have some problems unifying, the two way I learned how a Bose condensate appears. The main problem is that the observables seem to be quite different. In statistical physics lecture one starts with ...
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Why do composite bosons form a BEC?

I found this question here but it does not fully answer my question. The answer there was that "composite bosons can occupy the same state when the state is spatially delocalized on a scale larger ...
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What is the criteria of trapped ideal gas to form Bose-Einstein condensate (BEC)?

If we have ideal gas of bosons in a trapped harmonic potential, is the only necessary thing for BEC is a temperature less than the transition temperature? Or is there any other things we should keep ...
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What happens when we cool down the gas of non-identical particles?

For gas of identical particles, when we cool it down to extremely low temperature we can see one of two types of behaviour depending on the symmetry of wavefunction with respect to argument ...
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Order parameter and Bose-Einstein condensation

I want to study about order parameter and symmetry breaking related to bose einstein condensation in interacted system. Which book i should read? also i want to learn this in second quantization ...
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Free energy of non-interacting bosons in mean field

The result As a mathematician I am currently struggling to understand Tóth's Phase transition in an interacting Bose system. An application of the theory of Ventsel' and Freidlin. The free energy (...
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What are the anti-commutation relations needed to be fulfilled by fermionic Bogoliubov transformation?

Bogoliubov transformations are a well used tool to get rid off interaction terms in second quantized Hamiltonians. I'm interested in the fermionic Bogoliubov transformation used in BCS theory, e.g. \...
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Is the ground state a Schrödinger cat state?

Consider the following Bose-Hubbard Hamiltonian which describes a Bose-Einstein condensate confined in a two-well potential: $$ H= -T(a_L^\dagger a_R + a_L a_R^\dagger ) + \frac{U}{2}(n_L^2+n_R^2-...
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What is the super-bunching effects of composite boson?

What is the super-bunching effects of composite boson ?
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In what conditions we can take ground state energy $E_0$ equal to zero?

Like in 3D harmonic oscillator , $E_m = {h} \omega {(m_x +m_y + m_z + 3/2)}$, At ground state energy $m=0$ and $ E_m = h \omega(3/2)$. While discussing Bose-Einstein condensation, for calculations we ...
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Bose condensate in 4d

Could a boson gas condensate in a hypervolume $V$ in 4D? How can I find its critical temperature and the heat capacity? In the books it just said volume $V$, it does not specify the dimension. My ...