Bath-Induced Quantum Entanglement and Dispersion Forces

**Bath-Induced Entanglement: **Environment effects generally hamper or completely destroy the “quantumness” of any complex system. Particularly fragile against environment effects is quantum entanglement (QE) in multipartite systems. This fragility may disable quantum information processing and other forthcoming quantum technologies: interferometry, metrology and lithography. This QE fragility has been the standard resolution of the Schroedinger-cat paradox: the environment has been assumed to preclude macrosystem entanglement.

But is it inevitable that Schrödinger cats die of decoherence (as commonly believed)? Or, conversely, can a cat be both dead and alive in a thermal bath?

We shed light on these fundamental issues within the simple model of N spin-1/2 non-interacting particles that identically couple to a thermal oscillator-bath via the z-component of their spin (Pauli) operators. A single spin in such a model undergoes bath-induced pure dephasing. Yet, strikingly, an initial product state of N z-polarized spins can spontaneously evolve via such coupling to the bath, into a Schrödinger-cat state, also known as a macroscopic quantum superposiion (MQS) or GHZ state, nearly deterministically.

Thus, we show that QE in multipartite systems may *naturally (spontaneously)** *arise (albeit over limited time) in commonly encountered thermal environments (baths). This includes the spontaneous formation of Schroedinger-cat states, also known as macroscopic quantum superposition (MQS) states.

This comes about because their quantized collective dynamics can be mapped onto that of angular momentum (spin) ⃗with large eigenvalues. The finite spectral width (non-Markovian features) of most commonly encountered baths drives the spin ensemble into an entangled state, via effectively nonlinear dynamics.

*Schematic view of a product-state spin-polarized ensemble (left) that spontaneously evolves in the bath into an entangled MQS or GHZ (Schrödinger-cat) state at a particular time, as a result of bath-induced entanglement.*

**Our selected publications on these issues:**

Rao, Ddb; Bar-Gill, N; Kurizki, G (2011). Generation of Macroscopic Superpositions of Quantum States by Linear Coupling to a Bath. *Physical Review Letters.* 106

Bar-Gill, N; Rao, Ddb; Kurizki, G (2011). Creating Nonclassical States of Bose-Einstein Condensates by Dephasing Collisions. *Physical Review Letters.* 107

Shahmoon, E; Kurizki, G; Fleischhauer, M; Petrosyan, D (2011). Strongly Interacting Photons in Hollow-Core Waveguides. *Physical Review A.* 83

**Long-range bath-induced dispersive interactions: **The key to bath induced entanglement (BIE) is virtual quanta exchange via the bath. In free space the mode functions of the photonic bath are 3d plane waves, giving rise to real and virtual quanta exchange which both decay with interatomic separations r and correspond to Dicke-like cooperative emission/absorption and to cooperative Lamb shifts (i.e. resonant dipole–dipole interaction—RDDI), respectively. Whereas for interatomic separations *r* longer than the resonant atomic wavelength the real- and virtual-photon processes are comparable (scaling as *1/r*), in the near-field zone, i.e. for small r, the RDDI retains the familiar dipole-dipole scaling as *1/r** ^{3}* and can greatly exceed cooperative decay. Therefore, only in the near-field zone can free-space RDDI lead to predominantly deterministic BIE. In contrast, RDDI-induced entanglement is never deterministic at separations beyond the emission wavelength, where incoherent absorption and emission render it probabilistic.

**Our selected publications on these issues:**

Shahmoon, E; Mazets, I; Kurizki, G (2014). Non-Additivity in Laser-Illuminated Many-Atom Systems. *Optics Letters.* 39:3674-3677

Shahmoon, E; Kurizki, G (2014). Nonlinear Theory of Laser-Induced Dipolar Interactions in Arbitrary Geometry. *Physical Review A.* 89

Shahmoon, E; Mazets, I; Kurizki, G (2014). Giant Vacuum Forces Via Transmission Lines. *Proceedings of the National Academy of Sciences of the United States of America.* 111:10485-10490

Shahmoon, E; Kurizki, G (2013). Dispersion Forces Inside Metallic Waveguides. *Physical Review A.* 87

Shahmoon, E; Kurizki, G (2013). Nonradiative Interaction and Entanglement Between Distant Atoms. *Physical Review A.* 87

E. Shahmoon, P.Grising, HP Stimming, I. Mazets and G. Kurizki, Highly Nonlocal Optical Nonlinearities in Atoms Trapped Near A Waveguide, Optica 3, 725 (2016).

Zwick, A; Alvarez, Ga; Bensky, G; Kurizki, G (2014). Optimized Dynamical Control of State Transfer Through Noisy Spin Chains. *New Journal of Physics.* 16