# Quantum physics practical work with WAINTEACH

### 1. Spin resonance and Zeeman effect

The NV centre of a diamond has an electron spin S=1. Therefore, three fine levels can be distinguished, corresponding to the projection of the spin on the axis of the NV centre, |𝑚_𝑠=0, ±1⟩.

When illuminated with a green laser, the spin of the NV centre is pumped into the state, |𝑚_𝑠=0⟩, which emits more light than the states, |𝑚_𝑠=±1⟩. If we sweep the frequency of a microwave, we observe a drop in light when it is resonant with the transition |𝑚_𝑠=0⟩ ↔|𝑚_𝑠=-1⟩ or |𝑚_𝑠=0⟩ ↔|𝑚_𝑠=+1⟩.

In zero magnetic field, |𝑚_𝑠=-1⟩ and |𝑚_𝑠=+1⟩ are merged. Only one resonance frequency is then observed. By applying a magnetic field, the degeneracy is lifted between |𝑚_𝑠=-1⟩ and |𝑚_𝑠=+1⟩, and the lifting of the degeneracy is proportional to the projection of the magnetic field on the N-V axis.

In a diamond doped with the four orientations, students can observe four families of two lines, whose separation varies with the magnetic field.

### 2. Observation of hyperfine coupling

By studying a resonance line more closely, students can observe that it actually corresponds to three distinct lines. These transitions highlight the hyperfine coupling between the electron spin S=1 and the nuclear spin I=1 of the nitrogen atom in NV (14N ).

### 3. Longitudinal relaxation time T1

The longitudinal spin relaxation time – or T1 – characterises the time to return to thermodynamic equilibrium for an out-of-equilibrium NV centre, for example prepared in the |m_s=0⟩ state.

After a pumping time, the laser is switched off for a period of time. The laser can then be switched on again and the amount of light emitted from the NV centre observed. By varying the time without the laser, students can observe the return to equilibrium and measure the time T1.

### 4. Rabi oscillations

At a given magnetic field, it is possible to excite only one of the |m_s=0⟩ ↔|m_s=-1⟩ or |m_s=0⟩↔|m_s=+1⟩ transitions, by fixing the microwave frequency. At fixed power, students can vary the interaction time between the NV and the microwave field, and thus observe Rabi oscillations. It is then possible to study the evolution of these oscillations as a function of frequency detuning or by changing the microwave power.

### 5. Ramsey fringes

Students can also observe Ramsey fringes, and their blurring due to decoherence. The quantum coherence time – or T2* – characterises the rate at which a state superposition is destroyed, and corresponds to the decay time of the Ramsey fringe envelope.