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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Superfluid Dark Matter

Could the copious amounts of dark matter actually being comprised of axions that behave like a superfluid (bosonic) at the cosmological scale, but condensing out into a "normal" fluid at the ...
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How to convert absorption/emission rate of a molecule from cross section units (or molar extinction units) to frequency units?

I try to find relation how absorption/emission rate of molecules is expressed in different types of units? For example, I found that for Rhodamine 6G the peak absorption rate (in terms of molar ...
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Describing vortices using Gross-Pitaevskii equation

A lot of the description of vortices starts by saying a vortex in a Bose-Einstein condensate can be generated by imparting an angular momentum to the container. So as I understand it is described by ...
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Why Bose-Einstein condensate is superconducting

Im looking into Quantum Computing, where the BCS Theory is used to build Qubits with a BEC. Why does the Bose-Einstein Condensate not interact with other particles and hence has no dissipation? In ...
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Relativistic Bose-Einstein Condensation (BEC)

I wonder if there is a concept similar to the one of BEC but arising from Quantum Field Theory instead that from the usual one developed in non-relativistic many-body Quantum Mechanics. In non-...
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Double Potential Well (Hubbard Model)

The Hamiltonian from the Hubbard model for the double well potential $V(x) = V_0 \frac{x^2 - q^2}{q^2}$ is given by \begin{equation} H = -J(a_L^\dagger a_R + a_R^\dagger a_L) + \frac{U}{2} (a_L^\...
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Can Bose–Einstein condensate (BEC) take up no space?

If multiple bosons can occupy the same state, does that mean you can put an infinite number of them in a fixed container at zero temperature without pressure.
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Closed form solution of the normal density of a superfluid for the Bogoliubov spectrum

I've been trying to solve the following definite integral $$ \int_0^\infty dx\, x^4\, \frac{e^{\sqrt{x^4+2 x^2}/Tp}}{\left(e^{\sqrt{x^4+2 x^2}/Tp}-1\right)^2}\, ,\quad Tp = \frac{T}{Un} $$ This is the ...
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What does this simplification in the dipole-dipole energy of a droplet system mean?

I'm working on this paper for my BSc thesis. Specifically, I'm trying to obtain the the second part (DDI energy) of equation (05) on it. Usually, the DDI energy is obtained by $$E_{dd}=\frac{1}{2}\...
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Two different to do Bogobliubov transformation but sees to be contradictary

When try to do bogoliubov transformation on a weak-interaction cold atoms with uniform velocity $\vec{v}$, I used two different approaches, giving two different results. The Hamiltonian is $$\hat{H}=\...
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Why is Rubidium-87 used for Bose-Einstein condensates?

Rubidium-87 was the first and the most popular atom for making Bose–Einstein condensates in dilute atomic gases. Even though rubidium-85 is more abundant, rubidium-87 has a positive scattering length, ...
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Could a cloud of hydrogen-1 or helium-4 turn into Bose–Einstein condensate when the universe reaches maximum entropy?

Laboratories can cool clouds of hydrogen-1 and helium-4 respectively into Bose–Einstein condensate (BEC), while hydrogen-1 makes up 75% of all atomic matter in the observable universe and helium-4 ...
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Can multiple Helium-4 nuclei occupy the same place because the nuclei are bosonic?

A quarter of all matter in the observable universe is Helium-4 while all Helium-4 atoms have a nucleus with a zero spin integer which is characterized by Bose–Einstein statistics. Does this mean that ...
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What do scientists mean when they talk about two-dimensional photon gas in Photon BEC?

In a photon BEC, people are talking that cavity consisting of $2$ highly reflective mirrors make the photon gas $2$ dimensional by freezing out one wavevector $k_z$, which stays constant: $$ k_z=n\pi/...
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Complex Ginsburg-Landau equation for polaritons: adiabatic elimination of reservoir density

The review article 'Quantum fluids of light' focuses on exciton-polaritons in semiconductor microcavities. I don't understand the adiabatic elimination of the reservoir density $n_R$ performed on page ...
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Is Photon BEC possible in planar cavity?

It is well known result that Photon BEC was achieved in slightly curved cavity, because curved mirrors provide trapping potential (https://www.nature.com/articles/nature09567). We can see that this is ...
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What wavelengths are used practically in optical trapping?

I am currently working on my Master thesis in a cold atom research group, and have irritatingly found -- or rather not found -- that no book or paper seems to explicitly mention what wavelengths are ...
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How to observe off-diagonal long range order in superfluid?

off-diagonal long range order in superfluid is an effect that the matrix element of the single particle's density matrix remains finite in the long distance limit. My question is: how to prove this ...
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How is the phase of a BEC changing when some particles are being removed?

I have some trouble understanding what happens to the phase of a BEC when some particles are removed. The motivation of the question is the experiment of observing interference between two BECs. In my ...
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Why dilute gases do not form crystals at low temperatures?

I was wondering why a dilute gas (e.g. rubidium) forms a BEC at low temperatures rather than a crystal. My (naive) reasoning goes as follows: The dominant interaction between two atoms at low ...
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What is the Festina Lente Regime?

I am studying BEC formation without evaporative cooling, so realized only thrpugh optical means. One of the problems to face is "photon reabsorption": an atom absorbs a photon of the laser ...
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Why is a laser used to split a BEC in half?

In a youtube video, a German physicist Wolfgang Ketterle showed that two halves of the condensate creates interference pattern as though they are waves. I paused the video but still unable to ...
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Are all of the objects that composed the Bose-Einstein condensates absolutely can't be distinguished from each other?

Are all of the objects (e.g. photons or bosons) that composed Bose-Einstein condensates (BECs) literally can't be distinguished from each other? It was said several times on the Internet and many ...
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Interpretation of the condensate wavefunction

I am reading through the derivation of the Gross-Pitaevskii equation in the Heisenberg picture, and I am having some trouble interpreting the following identificiation. In the derivation the field ...
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Ideal Bose gas and Goldstone modes

In an ideal Bose gas there is a symmetry breaking phase transition, namely Bose-Einstein condensation. In a weakly interacting Bose gas or in helium-4 there is a longitudinal phonon because of the ...
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Under what conditions would neutrons pair up to produce bosons in the core of neutron star to form Bose-Einstein Condensates?

In Neutron star, the fermions get converted to bosons and form Bose-Einstein Condensates in its core. I couldn't find under what specific condition this phenomena takes place.
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Is there a difference between boson and bosonic?

I read about Bose-Einstein condensate consist of bosonic atoms at incredible low temperature do not obey Pauli exclusion, I am wondering what happens if it is possible to create fermionic photon for ...
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Why is the chemical potential of noninteracing bosons negative?

Chemical potential of noninteracting bosons is known to be negative because the Bose-Einstein distribution $[e^{(\epsilon-\mu)/T}-1]^{-1}$ should be free of singularities. However, I don't fully ...
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What does phonon exchange do in the theory of superconductivity?

In the theory of superconductivity, the phonon-mediated electron-electron scattering leads to an effective interaction, the BCS hamiltonian,$$\hat{H}_{\rm BCS}=\sum\limits_{\vec k,\sigma}\epsilon_{\...
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Variation of free energy vs. order parameter

In the paper M. Holzmann, G. Baym, Phys. Rev. B 76, 092502 (2007) the following formula (Eq. (18)) is given for a Bose-condensed system: $$ V\delta F=-\frac12\int d\mathbf{r}d\mathbf{r}'\:\delta\...
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Imaginary time propagation , Gross-Pitaevskii equation

When deriving the Gross-Pitaevskii equation we already assume that all the atoms are in the ground state. Based on this assumption, we minimize the energy functional and get the Gross-Pitaevskii ...
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Diagrammatic calcilation of superfluid and normal densities

Superfluid $\rho_\mathrm{s}$ and normal $\rho_\mathrm{n}$ densities in a Bose-condensed system can be calculated microscopically from the current-current response function $\chi_{\alpha\beta}(\mathbf{...
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Energy of BEC in terms of temperature

I have the formula for the energy of a Bosons gas $$ E(T) = \int_0^{\infty} d\epsilon \frac{4\pi}{2} \frac{V}{(2\pi)^3} (\frac{2m}{\hbar^2})^{3/2} \frac{\epsilon^{3/2}}{e^{-\beta\mu}e^{\beta\epsilon}-...
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BCS theory: where did all the bosons go?

After perusing BCS theory, I am perplexed by a seeming inconsistency. On the one hand, at the motivational level, it introduces bound, hence bosonic, Cooper pairs, which justify condensation ...
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Quantum vacuum fluctuations in BEC

I'm trying to understand Jeff Steinhauer's experiment and for some steps I don't see how it works physically. But generally, why the quantum vacuum fluctuations are guaranteed by the underlying ...
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Help with the derivation of the Gross-Pitaevskii equation

I'm having some difficulty deriving the gross pitaevskii equation using Heisenberg's equation of motion. I know that the many body hamiltonian is given by $$ \hat{H}=\int \left ( \frac{\hbar ^2}{2m} \...
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Are the definition of superfluid order parameter in real space and $k$-space same?

Considering fermions tight bind model,in real space the superfluid order parameter can be writed as $$\Delta=g\langle c_{i \uparrow}c_{i\downarrow}\rangle$$ In k space, the definetion of ...
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Gross-Pitaevskii equation and healing length

I am given the following GPE: $$-\frac{\hbar^2}{2mr}\frac{d}{dr} \Big( r \frac{d\chi}{dr} \Big) + \frac{\hbar^2}{2mr^2} \chi + (U_0 \chi^2-\mu)\chi=0.$$ I am asked to derive the healing length (not ...
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Why entropy in ideal BEC is independent of density

I am confused about one statement from the book Bose-Einstein Condensation in Dilute Gases. In the chapter discussing superfluid, the auther claims: The pressure and the entropy density $\frac{S}{V}$ ...
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Analogue black hole

I'm trying to understand the articles of Jeff Steinhauer Observation of quantum Hawking radiation and its entanglement in an analogue black hole and Observation of thermal Hawking radiation and its ...
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Why can't a gas of photons reach a Bose-Einstein condensate?

I have read in many places that as the gas of photons has a chemical potential $\mu=0$ it can't reach a Bose-Einstein condensate (BEC), but I don't understand why. I am reading Greiner's "...
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Unnecessary constraint in quantum statistics

In deriving Bose-Einstein or Fermi-Dirac distribution, if $N_n$ is no. of entities with energy $E_n$, then two the constraints for a system with N particles and total energy E are: $\sum_{n=1}^{\...
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BEC in two dimensions with interactions

For noninteracting 2D system of bosons, many textbooks have a statement that no BEC exists as the system is capable to accommodate infinite number of bosons when chemical potential $\mu \rightarrow 0 $...
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How is Einstein-Bose condensation supposed to stabilize d*(2380)?

A recent paper suggests a new dark matter candidate: Einstein-Bose condensates of the hexaquark/dibaryon d*(2380) ($uuuddd$). The nice thing about this theory is that it does not require any new ...
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Question regarding the derivation of equation for anomalous density

I was reading this paper and have a question regarding the derivation of equation $3.7$ for $\tilde m$ from equation $3.4c$. In particular, I was having trouble seeing why \begin{align} (h^\text{sp}(\...
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Gross-Pitaevskii equation invariants

Having the dimensionless GPE to model a BEC with harmonic plus optical potential, given by: $$i\frac{\partial{\psi}}{\partial{t}} = -\frac{1}{2}\nabla^2\psi(x,t) + V(x)\psi(x,t) + \frac{4\pi a_s N}{\...
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Thermalization of BEC dark matter

In the context of BEC/superfluid dark matter, one of the important requirements is that - within galaxies - dark matter thermalizes [1]. Axions are appropriate in this regieme, as their self-...
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Number density of phonons in superfluid

I'm reading Superfluidity and Superconductivity by Tilley & Tilley. In section 2.4, the argument is made that the normal component of superfluid helium consists of phonons and rotons. The ...
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What are the differences and similarities between Quantum synchronization and Bose condensation?

I am learning about Quantum synchronization and read [1,2] yesterday, which are about many-body bosonic systems. I understand that what happens when the system synchronizes, is that the destruction ...
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Quantum gravity experiment with BEC

This paper Exploring the unification of quantum theory and general relativity with a Bose-Einstein condensate proposes using a BEC in a superposition of two locations to test gravitationally-...

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