Creating superimposed states in an Hydrogen Atom

[Julian Blair]

I've been following the EdX course on Quantum Computing by Prof. Vazirani and I don't understand how one physically can create a superimposed state of the ground and 1st excited state of an hydrogen atom. He mentions "the use of light," but doesn't explain the frequency of the light, nor the length of the pulse.
Can anyone explain this for me?

Also, I don't understand the energy considerations when the hydrogen in a superimposed state is measured and found to be in either the ground state or the 1st excited state. Where did the energy either come from (excited state), or disappear (ground state.) ?

 

[DrClaude]

I've been following the EdX course on Quantum Computing by Prof. Vazirani and I don't understand how one physically can create a superimposed state of the ground and 1st excited state of an hydrogen atom. He mentions "the use of light," but doesn't explain the frequency of the light, nor the length of the pulse.
Can anyone explain this for me?

That would be the Lyman-α line in hydrogen, in the UV at λ = 121.57 nm. There are different methods to generate pulses that will produce a certain superposition of states. Look for instance at http://en.wikipedia.org/wiki/Rabi_problem

From the point of view of quantum computing, unless you are actually doing experiments, the actual details of how certain superpositions or manipulations of qubits are achieved is usually not important.

Also, I don't understand the energy considerations when the hydrogen in a superimposed state is measured and found to be in either the ground state or the 1st excited state. Where did the energy either come from (excited state), or disappear (ground state.) ?

The measurement process needs to be taken into account when considering conservation of energy.

 

[Julian Blair]

That would be the Lyman-α line in hydrogen, in the UV at λ = 121.57 nm. There are different methods to generate pulses that will produce a certain superposition of states. Look for instance at http://en.wikipedia.org/wiki/Rabi_problem

From the point of view of quantum computing, unless you are actually doing experiments, the actual details of how certain superpositions or manipulations of qubits are achieved is usually not important.The measurement process needs to be taken into account when considering conservation of energy.

That would be the Lyman-α line in hydrogen, in the UV at λ = 121.57 nm. There are different methods to generate pulses that will produce a certain superposition of states. Look for instance at http://en.wikipedia.org/wiki/Rabi_problem

From the point of view of quantum computing, unless you are actually doing experiments, the actual details of how certain superpositions or manipulations of qubits are achieved is usually not important.The measurement process needs to be taken into account when considering conservation of energy.

Dr. Claude:
Thanks for the reference to the Rabi Problem. Now I will have to try to understand that! As I understand Quantum Computing from Prof. Vazirani, manipulations of qubits via various gates is essential. My difficulty is in understanding how an electron can be in a quantum state with probabilities of being found in either of the two energy eigenstates. I was taught Quantum Chemistry many years ago, and we spent a lot of time talking about how many electrons were in the different quantum energy states. We never spoke about electrons that were in superimposed states in their individual atoms. Hopefully the Rabi problem will clarify that for me.
Could you please explain further your comment , "The measurement process needs to be taken into account when considering conservation of energy."? Are you indicating that the measurement process either adds or subtracts energy from the system so that Energy is conserved?

Thanks again,... Dr. Julian Blair

 

[DrClaude]

My difficulty is in understanding how an electron can be in a quantum state with probabilities of being found in either of the two energy eigenstates. I was taught Quantum Chemistry many years ago, and we spent a lot of time talking about how many electrons were in the different quantum energy states. We never spoke about electrons that were in superimposed states in their individual atoms.

You can understand a lot about the electronic structure atoms and molecules by considering single-particle states, orbitals, and filling them each with their own electron. But that is a very simplified picture. Take the two electrons in the ground state of helium: they are in a superposition of spin states: $(|\uparrow \downarrow \rangle - |\downarrow \uparrow \rangle)/\sqrt{2}$.

Could you please explain further your comment , "The measurement process needs to be taken into account when considering conservation of energy."? Are you indicating that the measurement process either adds or subtracts energy from the system so that Energy is conserved?

Generally speaking, yes.