Download The quantum world of ultra-cold atoms and light by Crispin Gardiner, Peter Zoller PDF

By Crispin Gardiner, Peter Zoller

This booklet is the 1st in a trilogy designed to make to be had to these operating in
the box, and to complex scholars, an entire suite of theoretical options wanted
for quantum applied sciences. those were constructed in the paradigm of
quantum optics, a box according to using atoms and light-weight. As contributors within the
theoretical points of quantum optics, ultra-cold atoms, and quantum
information, now we have labored either jointly and independently on lots of the major
themes that have arisen within the final thirty years, and through this era have either
taught periods and supervised examine initiatives within the box.

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23) One is to require that the other that aˆ |0 = 0, but aˆ † aˆ |0 = 0. 23) first. 9) of the annihilation operator and Schrödinger’s famous formula pˆ = −i ∂/∂q in the q representation, we obtain a differential equation for the wave function ψ0 (q) of the state |0 1 ∂ ψ0 (q) = 0. 26) +∞ (normalized to yield −∞ | ψ0 (q) |2 dq = 1). In the momentum representation we obtain the same formula for ψ0 (p) ψ0 (p) = π −1/4 exp − p2 2 . 27) In this way we have shown that a well-behaved state with precisely zero photons exists, called the vacuum state.

Rn ) of the atoms obeys the Schrödinger equation with the Hamiltonian ⎛ ˆ = H k h2 ∇ 2 ⎝− ¯ k + U(rk ) + 2m ⎞ V |rk − rk | ⎠ . k >k ˆ t) with the Bose commutation Let us define the quantum field ψ(r, relations ˆ t), ψˆ † (r , t) = δ(r − r ), ψ(r, ˆ t), ψ(r ˆ , t) = 0. ψ(r, 33 34 Quantum field theory of light We postulate that ψˆ obeys the field equation ih¯ ∂ ψˆ h¯ 2 ∇ 2 = − +U+ ∂t 2m ˆ ) dr ψˆ † (r ) V |r − r | ψ(r ˆ ψ. You will show that the quantum field ψˆ is equivalent to the Schrödinger wave function ψ(r1 , .

The reason for this power law is the scaling of the zeropoint energy: suppose we extend the cavity size by a scaling factor η. 39) of the cavity would be reduced by η−1 ; the zero-point energy would be reduced by the same factor; and so the zeropoint energy per area scales with η−3 . Therefore, the Casimir force per area depends on a−4 . , 2001). 50). Zero-point energy is real, despite its infinity. 47) is infinite, but we treated it as a finite quantity. All of these dubious features are artefacts, one can avoid them, apart from one fundamental assumption: the zero-point energy of the electromagnetic field in empty space is constant, with finite energy density, for reasons as yet unknown.

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