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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Fugacity in Bose-Einstein condensate

Just a simple question, I didn't manage to find out in my books... The fugacity $z = e^{\beta \mu}$ in the case we have condensation in a bose statistics. Is it always 1 or $z \to 1$? In the ...
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Can we have Bose condensation for bosons satisfying a dispersion relation $E=Cp^s$ $\forall$ s?

Suppose a dispersion relation $E=Cp^s$ where $C$ is a constant is known for a collection of massive non-interacting bosons. What is the way to find out whether there will be Bose-Einstein condensation ...
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Why doesn't the four-gluon vertex give mass to gluons?

We have a four-gluon vertex and a gluon vacuum condensate. Why doesn't this provide us with gluon masses, as in the NJL model where the condensate gives rise to an effective mass term?
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How do I evaluate the angular momentum of the wave function?

I'm working with Bose-Einstein condensates and running a 2D single component Gross-Pitaevskii equation solver for the simulations in MATLAB. The way it works is that it numerically solves the GP ...
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Why is a collection of non-interacting bosons pathological?

In this lecture titled "Disorder and Interactions: From Spin Chains to Cold Atoms" the speaker Thierry Giamarchi claims that a collection of non-interacting bosons is totally pathological. His argues ...
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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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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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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 Grand canonical ensemble

Why we develop formalism of Bose Einstein Condensation in framework of grand canonical ensemble ?
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Bosonic qubits using BEC versus usual qubit implementations based on energy levels

All condensate atoms in a BEC (say like Rb, etc) effectively occupy the lowest energy-state. If it is that the case, then how are such bosons in a BEC encoded as a qubit? In particular, when Grover ...
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Hamiltonian with Dirac Delta function

I've to compute this expression $$ \hat{H} ~=~\frac{1}{4}g_2\int d^3R\int d^3r\ \bar{\Psi}(\vec{R}+\frac{\vec{r}}{2})\bar{\Psi}(\vec{R}-\frac{\vec{r}}{2}) $$$$ \times \left[ \delta(\vec{r})\nabla_{\...
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Would dark matter (as a BEC) be captured by Black Holes, Neutron Stars, etc?

Suppose that dark matter is in the form of a Bose-Einstein Condensate, with a DeBroglie wavelength of ~10,000 LY. (There are some axion models of DM where the axions are in a BEC.) In this model, the ...
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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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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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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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Bose Einstein condensates and gravity

Are Bose Einstein condensates affected by gravitational attraction ? In sufficient quantity, do Bose Einstein condensates exert a gravitational force ?
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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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What is the probability that a single-particle bosonic quantum state is occupied?

Unlike the Fermi-Dirac distribution function, the Bose-Einstein distribution function $$f(E)=\bar n_r=\frac{1}{e^{\beta(E-\mu)}-1}$$ can be greater than 1, and therefore, doesn't represent a ...
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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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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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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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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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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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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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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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Is Mott insulator the same as non-compressible quantum fluid?

In the field of ultracold quantum gases we study the so called Bose-Hubbard model given in second quantization: $$\hat{\mathcal{H}} = -t\sum_{\langle i,j\rangle}\hat{a}^{\dagger}_{i}\hat{a}_{j} + \...
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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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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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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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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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Bose-Einstein condensation in 1D harmonic oscillator and its density of states

I have troubles understanding how (and whether) Bose-Einstein condensation works in 1-D harmonic oscillator. From my calculation it seems that in limit of infinite number of particles, almost all of ...
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Why do we use grand canonical ensemble for BEC description?

The system we consider has constant $N$, $V$ and $T$ (the number of particles, volume and temperature) This is just the thermodynamic variables for the canonical ensemble, why we use fugacity $z$ or ...
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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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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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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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Does the Hong-ou-Mandel effect happen within a delay equal to the coherence time of the two photons?

I read that photon bunching happens for thermal light within the coherence time of the thermal light. That is, if the time for detection is greater than the coherence time of the thermal light, no ...
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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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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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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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Can I distinguish a Bose-Einstein Condensate of composite bosons from one of elementary bosons?

The only requirement for an ensemble of particles to undergo a transition into a BEC is to be bosons. But two fermions also make a bosons. Are there physical, measureable implications of a BEC being ...
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physics of the beaker experiment for superfluid helium

here is an illustration and explanation of the beaker experiment over superfluid helium: So, according to this experiment, can anyone say what is the cause? I mean the superfluids are disconnected ...
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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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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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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 ...