Pulse sequence design protocol
Systems and methods are disclosed for a pulse sequence that reduces disorder and/or interaction effects in spin systems. A protocol can be used to design a pulse sequence that includes altering the frame orientation of the spin system with each electromagnetic pulse in the pulse sequence. The frame orientations during the sequence can conform to certain conditions. The number positive rotations along each axis can be the same as the number negative rotations along the respective axis. The number of rotations along one axis should be the same as the number of rotations along the other axes.
1. A method of reducing disorder and interaction effects in a spin system, the method comprising:
applying a sequence of electromagnetic pulses to the spin system, the spin system having a frame orientation in an evolution period τ 0 before a first pulse k=1 of the sequence of electromagnetic pulses; and
altering the frame orientation of the spin system with each electromagnetic pulse in the sequence of pulses, each electromagnetic pulse being one or more of a π/2 rotation or a π rotation, the frame orientations during the sequence conforming to the following relations:
∑
k
F
μ
k
τ
k
=
0
,
and
∑
k
F
x
k
τ
k
=
∑
k
F
y
k
τ
k
=
∑
k
F
z
k
τ
k
,
where F μk represents the frame orientation of the spin system in a respective evolution period of duration τ k after pulse k for each spin direction μ=x, y, z, and where k=0 corresponds to the frame orientation F μ0 in the evolution period before the first pulse k=1.
2. The method of claim 1 , wherein the sequence of electromagnetic pulses is periodic, and the pulses are equally spaced.
3. The method of claim 1 , wherein at least one electromagnetic pulse of the sequence of electromagnetic pulses includes two or more π/2 rotations, and the spin system further comprises intermediary frame orientations representing the frame orientation of the spin system after each but a final π/2 rotation, the intermediary frame orientations conforming to the following relations:
∑
k
F
μ
v
=
0
,
∑
k
F
xv
=
∑
k
F
yv
=
∑
k
F
zv
where F μv represents the frame orientation of the spin system for each intermediary frame v for each spin direction μ=x, y, z.
4. The method of claim 1 , wherein for each π rotation, the frame orientation of the spin system further comprises an intermediary frame orientation representing the frame orientation of the spin system after the first π/2 rotation of the π rotation, intermediary frame orientations together conforming to the following relations:
∑
k
F
μ
v
=
0
,
∑
k
F
xv
=
∑
k
F
yv
=
∑
k
F
zv
where F μv represents the frame orientation of the spin system for each intermediary frame v for each spin direction μ=x, y, z.
5. The method of claim 1 , wherein for each pair of axes μ,μ=x, y, z, the parity of frame changes sums to zero such that
∑
k
F
μ
,
k
F
v
,
k
+
1
+
F
μ
,
k
+
1
F
v
,
k
=
0
,
for (μ, v)=(x, y), (x, z), (y, z).
6. The method of claim 1 , wherein the chirality of frame changes sums to zero such that the cyclic sum
∑
k
F
->
k
×
F
→
k
+
1
=
0
→
,
where {circumflex over (F)} k =Σ u F μ,k {right arrow over (e)} μ and {right arrow over (e)} μ are the unit vectors along axis directions.
7. The method of claim 1 , further comprising:
generating an effective magnetic field {right arrow over (B)} eff as seen by the driven spins; and
initializing the frame orientation of the spin system to be perpendicular to the effective magnetic field.
8. The method of claim 1 , wherein the sequence of electromagnetic pulses is used to increase the coherence time of an ensemble of nitrogen-vacancy (NV) centers in diamond beyond a spin-spin interaction sensitivity limit.
9. The method of claim 1 , wherein the sequence of electromagnetic pulses is used to increase the coherence time of a magnetic field sensing ensemble of nitrogen-vacancy (NV) centers in diamond such that a sensitivity of the magnetic field sensing ensemble of NV centers overcomes a spin-spin interaction sensitivity limit.
10. A system, comprising:
a quantum sensor comprising an ensemble of spins in solid state, the ensemble of spins having a density in which the interactions between the spins limit a coherence time of the ensemble of spins in solid state; and
a pulse generator configured to apply electromagnetic radiation to the quantum sensor, the electromagnetic radiation decoupling the interactions between the spins to increase the coherence time beyond a spin-spin interaction sensitivity limit of the ensemble of spins when measuring a target signal.
11. The system of claim 10 , wherein the quantum sensor comprising an ensemble of NV centers in diamond of density r ppm, and the coherence time is increased to be longer than a value of 72/r us (as determined from the scaling of the interaction limit), up to 1 ms.
12. The system of claim 10 , wherein the pulse generator applies electromagnetic radiation to the quantum sensor according to the method of claim 1 .
13. A system comprising:
a spin system; and
a pulse generator configured to a sequence of electromagnetic pulses to the spin system, the spin system having a frame orientation in an evolution period τ 0 before a first pulse k=1 of the sequence of electromagnetic pulses, each electromagnetic pulse corresponding to a frame of the sequence of pulses, and each electromagnetic pulse being one or more of a π/2 rotation or a π rotation, the frame orientations during the sequence conforming to the following relations:
∑
k
F
μ
k
τ
k
=
0
,
and
∑
k
F
x
k
τ
k
=
∑
k
F
y
k
τ
k
=
∑
k
F
z
k
τ
k
,
,
where F μk represents the frame orientation of the spin system in a respective evolution period of duration τ k after pulse k for each spin direction μ=x, y, z, and where k=0 corresponds to the frame orientation F μ0 in the evolution period before the first pulse k=1.
14. The system of claim 13 , wherein the sequence of electromagnetic pulses is periodic, and the pulses are equally spaced.
15. The system of claim 13 , wherein at least one electromagnetic pulse of the sequence of electromagnetic pulses includes two or more π/2 rotations, and the spin system further comprises intermediary frame orientations representing the frame orientation of the spin system after each but a final π/2 rotation, the intermediary frame orientations conforming to the following relations:
∑
k
F
μ
v
=
0
,
∑
k
F
xv
=
∑
k
F
yv
=
∑
k
F
zv
where F μv represents the frame orientation of the spin system for each intermediary frame v for each spin direction μ=x, y, z.
16. The system of claim 13 , wherein for each π rotation, the frame orientation of the spin system further comprises an intermediary frame orientation representing the frame orientation of the spin system after the first π/2 rotation of the π rotation, intermediary frame orientations together conforming to the following relations:
∑
k
F
μ
v
=
0
,
∑
k
F
xv
=
∑
k
F
yv
=
∑
k
F
zv
where F μv represents the frame orientation of the spin system for each intermediary frame v for each spin direction μ=x, y, z.
17. The system of claim 13 , wherein for each pair of axes μ,μ=x, y, z, parity of frame changes experienced by the spin system sums to zero such that
∑
k
F
μ
,
k
F
v
,
k
+
1
+
F
μ
,
k
+
1
F
v
,
k
=
0
,
for (μ, v)=(x, y), (x, z), (y, z).
18. The system of claim 13 , wherein chirality of frame changes experienced by the spin system sums to zero such that the cyclic sum
∑
k
F
->
k
×
F
→
k
+
1
=
0
→
,
where {circumflex over (F)} k =Σ μ F μ,k {right arrow over (e)} μ and {right arrow over (e)} μ are the unit vectors along axis directions.