Questions tagged [optical-lattices]

A lattice formed by the interference of counter-propagating laser beams, creating a spatially periodic polarisation pattern, which may be used to trap neutral atoms via the AC Stark shift to perform quantum simulation experiments or build atomic clocks.

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Response function in a honeycomb lattice

My doubt is the following: If we calculate the response function of a honeycomb lattice in the three spatial directions, the xx components will be always equal to yy. I imagine that it is because of ...
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What does "address" mean in "addressing lattice sites"?

In an abstract about "Sub-lattice-resolved imaging", the author was talking about local addressing of individual lattice sites: Here we introduce an imaging approach where matter wave ...
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Bloch's theorem on $x$-$y$ coupled potential

Say I have the following lattice potential: $$V(x,y)= V_0\left(\cos ax+\cos by+\cos(ax+by)\right)$$ This is a periodic function of $x$ and $y$, so Bloch's theorem is applicable... I want to use it to ...
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Maximum delocalization of two bosons in a double-well system (Bose-Hubbard model)

I'm studying optical lattice, and I have a question with respect to the Bose-Hubbard model. The situation is as follows: two identical spinless bosons are in a double-well system. For your convenience,...
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Is it possible to laser cool without using spatially-varying magnetic fields and above zero degrees?

As the title says, is it possible to laser cool without generating a weak quadrupolar magnetic field? Also, if I wasn't trying to achieve extremely low temperatures is it possible to use laser cooling ...
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Time-independent constant-Hamiltonian Schrodinger equation solution when at time 0 there's a matrix with mostly 0s?

So, I'm trying to model the behavior of a particle in a 2D optical lattice. I've done it successfully for 1D. I'm using the time-dependent Schrodinger equation with a constant Hamiltonian, so $\Psi(t)=...
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Can the Jaynes-Cummings model serve as photon induced particle hopping?

If you have an electron in a cavity and it has a ground state and an excited state which are somehow localized in either site of the cavity, does this mean that you can describe this situation as ...
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Determine Phase and Group Velocities for Monoatomic Lattice

I have a question about determining the phase and group velocity for a monoatomic lattice. I know from various reference texts that $$v_p = \frac {\omega}{q}$$ $$v_g = \frac {\partial \omega}{\partial ...
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Equivalence between rotation and magnetic flux in lattice models

I am trying to understand the presence of complex hopping amplitudes in Hubbard-like lattice models. The hopping term features the so called "Peierls phase": $$ - t\sum_{j=1}^L \left( c_{...
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How to understand produce optical standing wave by mirror reflecting with half-wave loss

Considering the incident optical wave $E_i=e^{ikx}$ and reflect optical wave $E_r=e^{-ikx+i\pi}$,where $\pi$ corresponding the half wave loss.The superposition of incident wave and reflect wave is $E=...
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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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Lattice vs Superlattice

What is the difference between lattice and superlattice ? Can anyone describe with a schematic figure? I have encountered superlattice in the context of bose hubbard model. Also what are the ...
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Floquet bandstructure calculation

In this paper "Photonic Floquet Topological Insulators" the authors calculate the bandstructure of a time-periodic Hamiltonian. They create a time-dependent tight-binding Hamiltonian via the ...
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Optical lattices - spin

I know different potentials can be realised with spin dependent optical lattices. My question is, how do the optical lattices become spin dependent? I cannot find a good explanation on the literature,...
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Getting the Bose-Hubbard Hamiltonian from cold atoms

In the famous paper by Dieter Jaksch, it is shown that the usual Hamiltonian for cold bosonic atoms interacting by s-wave scattering (Equation (1) in the paper): $$ \hat{H}=\int d^3 x\hat{\psi}^\...
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Optical trapping: factor 1/2 in definition of gradient force and potential energy?

If one consider the original deduction of the gradient forces that is applied to the trapped particle we can find the following: $$F_{grad}=\frac{1}{4} \alpha \nabla E_0^2(r),$$ where $E_0(r)$ is an ...
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Reduced absorption coefficient question

I came across a paper that reads It is noteworthy that for a sample without lateral light propagation in the material, i.e. [reduced scattering] $\mu_s' = \infty$ and [absorption] $\mu_a=0$, ... ...
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In AMO experiments, how do cold alkali metal atoms remain gaseous?

My focus is on condensed matter physics, so I've never really explored this question although it always seemed curious to me. My "immediate reaction" intuition would dictate that cold metal atoms ...
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How do you find the 2nd order perturbed energy shift from the quantised dipole hamiltonian?

Without using the Rotating wave approximation how do you find the trapping potential $U(\mathbf r)$ experienced by an atom at position $\mathbf r$ for arbitrary laser frequencies? This can be done ...
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Why is matter wave field usually assumed to be be intrinsically stable?

In the paper "Collapse and revival of the matter wave field of a Bose-Einstein condensate" by M. Greiner, O. Mandel, T. Haensch and I. Bloch, it was stated that Bose-Einstein condensate (BEC) ...
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Energy conservation in Kapitza-Dirac diffraction?

In Kapitza-Dirac diffraction, a standing wave of light (wavevector of single wave $k$) is pulsed on for a very short period of time ($\sim \mu s$) onto a bunch of cold atoms. This results in the atoms ...
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Numerical solution of driven infinite well with Floquet matrix

I am trying to understand and replicate figure 3 of this paper. The idea is that we have our box with a periodic drive $$H(t) = \frac{p^2}{2m}-F_0x\cos(\omega t)$$ The author states In order to ...
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Symmetry breaking and Superfluid - Mott Insulator transition

I know my question is similar to what mentioned in this post: Symmetry breaking in Bose-Hubbard model. Yet, I don't find it clear. I've in mind a 1D Bose-Hubbard Hamiltonian. Moving from the Mott ...
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Is Bose-Einstein condensate in the optical lattice a single mode condensate?

I recently read about BEC loaded into the optical lattice p.200 Looking at a condensate released from a lattice after a time of flight typically on the order of a few milliseconds amounts to ...
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Time of flight images of Bose-Hubbard model

on the website of Immanuel Bloch, you can find time of flight images of bosonic particles inside an optical lattice for different values of the depth of the lattice. (http://www.quantum.physik.uni-...
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can I make an optical lattice with a non Ti:Sapphire laser?

I am currently at a small undergraduate institution that does not have access to workhorses like a Ti:Saphire laser, however I am very interested in trying to make an optical lattice with lower power ...
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Are Dirac points the norm for 2D band structure?

I've been doing simulations of band structure for 2D optical lattices, and something I've noticed is that, for sufficiently shallow lattices, there are typically points on the edge of the first ...
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Bose-Hubbard Parameters from Band Structure

Could someone explain me how to compute numerically the parameters J and U and $\mu$ and the Wannier functions in the Bose-Hubbard model: $H=J\sum\limits_{j,1}^{L-1} (a_j^{+} a_{j+1}+ a_{j} a_{j+1}^{+...
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How to add Langevin terms to the semiclassical Bose-Hubbard model?

I would like to add Langevin terms to the Hamilton equations of motion of the semiclassical Bose-Hubbard model. Here's what I have: I start with the standard example of Brownian motion, a particle ...
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Novel atomic clocks: can quantum and many-body effects help?

I am trying to learn if there are any proposals concerning the application of quantum and many-body effects to atomic clocks. From what I understand, optical lattices have been used for timekeeping ...
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Ground state symmetry breaking in Bose-Hubbard model with spin-orbit coupling

The Hamiltonian for 2D Bose-Hubbard model with spin-orbit coupling on a square lattice is written as $ H = -t\sum_{\langle ij \rangle}\Psi_i^{\dagger}\Psi_j^{\vphantom{\dagger}} + \frac{U}{2}\sum_{i\...
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Can one make a synthetic dimension "curl around" into a cylinder?

A really cool recent proposal, Synthetic Gauge Fields in Synthetic Dimensions. A. Celi et al. Phys. Rev. Lett. 112, 043001 (2014), arXiv:1307.8349, shows how you can simulate a synthetic magnetic ...
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