# What is the spin-boson model for decoherence in a Penning trap?

• I
• Malamala
In summary, the conversation discusses the application of decoherence to a Penning trap with a single ion at the center. The main focus is on the decoherence caused by black body radiation, and the conversation mentions the use of the spin-boson model to calculate the coupling constant. Some reading suggestions and previous calculations are requested. The response provides some equations and suggests taking the variance of the blackbody frequency shift to calculate the decoherence rate. However, the exact calculation method is still uncertain. The conversation also mentions the need for more information on the spin-boson model being used.
Malamala

Twigg, gentzen and asd789
Sorry for the slow and short reply.

I'm not 100% sure how to calculate the decoherence rate, but I can tell you that the blackbody radiation shifts the energy difference ##E_e - E_g## by ##\delta E = (\alpha_e - \alpha_g) \| \vec{E}_{BBR} \|^2## where ##\alpha_{e,g}## is the polarizability of the ground (excited) state (at a particular frequency). This is for Stark shifted qubit states. There is an analogous expression for Zeeman states. You can get ##\| \vec{E}_{BBR} \|^2## from Planck's law for blackbody radiation (spectral irradiance) and your trap's geometry.

My gut feeling is that you can get the decoherence rate by taking the variance of this blackbody frequency shift (##\gamma = \sigma_\nu##, same idea as when you calculate the coherence time of a laser from bandwidth). Thus, the decoherence rate would bee $$\gamma = |\alpha_e - \alpha_g| \sqrt{\langle \| \vec{E}_{BBR} \|^4 \rangle - \langle \| \vec{E}_{BBR} \|^2 \rangle^2}$$ The quadratic term can be calculated from the blackbody partition function by looking at the expectation value of energy squared (just as you do when you calculate energy fluctuations in an ideal gas from the heat capacity).

Does that make sense?

Also, I'm not sure which "spin-boson model" you're referring to. Is there a paper you're reading that you can link us to?

## 1. What is decoherence in a Penning trap?

Decoherence in a Penning trap is the process by which a quantum system loses its coherence and behaves more like a classical system due to interactions with its surrounding environment. In a Penning trap, this is caused by interactions with external electromagnetic fields and collisions with residual gas particles.

## 2. How does decoherence affect the behavior of particles in a Penning trap?

Decoherence causes the quantum states of particles in a Penning trap to become mixed, making it difficult to observe and manipulate individual quantum states. This can lead to the loss of quantum information and hinder the precision of measurements.

## 3. Can decoherence be controlled or minimized in a Penning trap?

Yes, decoherence can be controlled or minimized by carefully designing the trap and its surrounding environment. This can include reducing external electromagnetic fields, improving vacuum conditions to reduce collisions with gas particles, and using techniques such as quantum error correction to protect against decoherence.

## 4. What are the potential applications of studying decoherence in a Penning trap?

Studying decoherence in a Penning trap can help improve our understanding of quantum systems and their interactions with the environment. This knowledge can be applied to developing more precise quantum sensors, quantum computers, and other quantum technologies.

## 5. How is decoherence in a Penning trap related to the concept of quantum entanglement?

Decoherence in a Penning trap can lead to the loss of quantum entanglement between particles. This is because entanglement is a delicate quantum state that can easily be disrupted by interactions with the environment. Understanding and controlling decoherence is crucial for maintaining and utilizing quantum entanglement in experiments and applications.

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