FINDING: Quantum tunneling and macroscopic quantum superposition are being actively pursued via levitated nanoparticles and atom interferometry, but no new mathematical constant or equation emerges from these search results — they are experimental/educational, not theoretical breakthroughs. | MATH: No new equations or constants extracted. Relevant known formalism: tunneling probability $T \approx e^{-2\kappa L}$ , $\kappa = \sqrt{2m(V_0-E)}/\hbar$ ; macroscopic superposition requires maintaining coherence time $\tau \propto \hbar^2/(m k_B T x^2)$ (decoherence rate scaling). Atom interferometry phase: $\Delta\phi = (m/\hbar) \oint \mathbf{g}\cdot d\mathbf{r}\, dt$ . | CONNECTION: None directly stated. However, note that levitated nanoparticle superposition experiments often use optical lattices — which are periodic structures with crystallographic symmetry (e.g., 1D lattice spacing $d = \lambda/2$ — ratio 0.5, not golden). No 0.382/0.618/0.786/1.618/2.618 or base-60 appears in Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Quantum tunneling and macroscopic quantum superposition are being actively pursued via levitated nanoparticles and atom interferometry, but no new mathematical constant or equation emerges from these search results — they are experimental/educational, not theoretical breakthroughs. | MATH: No new equations or constants extracted. Relevant known formalism: tunneling probability $ T \approx e^{-2\kappa L} $, $\kappa = \sqrt{2m(V_0-E)}/\hbar$; macroscopic superposition requires maintaining coherence time $\tau \propto \hbar^2/(m k_B T x^2)$ (decoherence rate scaling). Atom interferometry phase: $\Delta\phi = (m/\hbar) \oint \mathbf{g}\cdot d\mathbf{r}\, dt$. | CONNECTION: None directly stated. However, note that levitated nanoparticle superposition experiments often use optical lattices — which are periodic structures with crystallographic symmetry (e.g., 1D lattice spacing $d = \lambda/2$ — ratio 0.5, not golden). No 0.382/0.618/0.786/1.618/2.618 or base-60 appears in Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Oct 19, 20260 citations

Quantum State Preparation In Optical Lattices

Ivan Deutsch, Poul Jessen

May 18, 19971 citation

Coherent quantum tunnelling and macroscopic superposition states in optical lattices

Ivan Deutsch, Poul Jessen

Summary form only given. The AC-Stark shift of a set of interfering laser beams together with the Zeeman interaction with external magnetic fields provide flexible mechanisms for coherently controlling atomic wave packets. When detuned far from atomic resonance, these optical lattices can trap cold atoms with minimal dissipation and thus provide an ideal environment for observing quantum coherent phenomena. We consider a one dimensional lattice of double wells produced by counterpropagating linearly polarized laser beams and a static magnetic field transverse to the laser wave vectors.Summary form only given. The AC-Stark shift of a set of interfering laser beams together with the Zeeman interaction with external magnetic fields provide flexible mechanisms for coherently controlling atomic wave packets. When detuned far from atomic resonance, these optical lattices can trap cold atoms with minimal dissipation and thus provide an ideal environment for observing quantum coherent phenomena. We consider a one dimensional lattice of double wells produced by counterpropagating linearly polarized laser beams and a static magnetic field transverse to the laser wave vectors.

Conference on Lasers and Electro-OpticsNov 27, 20020 citations

Quantum-state control in optical lattices

Ivan Deutsch, Poul Jessen

We study the means of preparing and coherently manipulating atomic wave packets in optical lattices, with particular emphasis on alkali-metal atoms in the far-detuned limit. We derive a general, basis-independent expression for the lattice potential operator, and show that its off-diagonal elements can be tailored to couple the vibrational manifolds of separate magnetic sublevels. Using these couplings one can evolve the state of a trapped atom in a quantum coherent fashion, and prepare pure quantum states by resolved-sideband Raman cooling. We explore the use of atoms bound in optical lattices to study quantum tunneling and the generation of macroscopic superposition states in a double-well potential. Far-off-resonance optical potentials lend themselves particularly well to reservoir engineering via well-controlled fluctuations in the potential, making the atom-lattice system attractive for the study of decoherence and the connection between classical and quantum physics.We study the means of preparing and coherently manipulating atomic wave packets in optical lattices, with particular emphasis on alkali-metal atoms in the far-detuned limit. We derive a general, basis-independent expression for the lattice potential operator, and show that its off-diagonal elements can be tailored to couple the vibrational manifolds of separate magnetic sublevels. Using these couplings one can evolve the state of a trapped atom in a quantum coherent fashion, and prepare pure quantum states by resolved-sideband Raman cooling. We explore the use of atoms bound in optical lattices to study quantum tunneling and the generation of macroscopic superposition states in a double-well potential. Far-off-resonance optical potentials lend themselves particularly well to reservoir engineering via well-controlled fluctuations in the potential, making the atom-lattice system attractive for the study of decoherence and the connection between classical and quantum physics.

arXiv:quant-ph/9801023Physical Review AMar 1, 1998243 citations

Quantum State Preparation In Optical Lattices

Jessen

Quantum Electronics and Laser Science ConferenceJan 1, 19970 citations

T \approx e^{-2\kappa L}

\kappa = \sqrt{2m(V_0-E)}/\hbar

; macroscopic superposition requires maintaining coherence time

\tau \propto \hbar^2/(m k_B T x^2)

(decoherence rate scaling). Atom interferometry phase:

\Delta\phi = (m/\hbar) \oint \mathbf{g}\cdot d\mathbf{r}\, dt

. | CONNECTION: None directly stated. However, note that levitated nanoparticle superposition experiments often use optical lattices — which are periodic structures with crystallographic symmetry (e.g., 1D lattice spacing

d = \lambda/2

— ratio 0.5, not golden). No 0.382/0.618/0.786/1.618/2.618 or base-60 appears in Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com