Method for reading the spin state of a system and associated method for determining the fidelity
A method of measuring the spin state of two charged particles able to adopt a first, second, third, and fourth spin state S, T+, T0 and T, the two charged particles being contained in a system, including first and second quantum dots characterised by a first parameter Γ relative to the potential barrier separating the two quantum dots and a second parameter ε corresponding to the difference in energy between the fundamental states of the first and second quantum dots, the couple formed by the values of these two parameters defining an operating point of the system as a function of which the system adopts a first charge state noted (1,1) wherein each quantum dot contains a charged particle, a second charge state noted (2,0) wherein the first quantum dot contains two charged particles or a third charge state noted (0,2) wherein the second quantum dot contains two charged particles.
1. A method for measuring a spin state of two charged particles being able to adopt a first spin state noted S, a second spin state noted T+, a third spin state noted T0 and a fourth spin state noted T−, the two charged particles being contained in a system, comprising a first quantum dot and a second quantum dot characterised by a first parameter Γ relative to a potential barrier separating the first and second quantum dots and a second parameter ε corresponding to a difference in energy between a fundamental state of the first quantum dot and a fundamental state of the second quantum dot, a couple formed by values of the first and second parameters defining an operating point of the system as a function of which the system adopts a first charge state noted (1,1) wherein each quantum dot contains a charged particle, a second charge state noted (2,0) wherein the first quantum dot contains two charged particles or a third charge state noted (0,2) wherein the second quantum dot contains two charged particles, the operating point of the system being initially in a first operating point corresponding to the first charge state (1,1) of the system and for which the first S, the second T+, the third T0 and the fourth T− spin states are eigenstates of the spin of the two charged particles, the method comprising:
a first step of modification of the operating point of the system during which the operating point is displaced from the first operating point to a second operating point corresponding to the second charge state (2,0) or to the third charge state (0,2), the energy level of the first spin state S and the second spin state T+ forming an avoided crossing during the displacement from the first operating point to the second operating point, the modification of the operating point taking place non-adiabatically during a passage of the avoided crossing such that, during said first step, the system transits from the first charge state (1,1) to the charge state corresponding to the second operating point when the two charged particles contained in the system are in the first spin state S and the system is maintained in the first charge state (1,1) for the other spin states;
a first step of measuring the charge state of the system, the spin state of the two charged particles at the first operating point being the first spin state S if the charge state of the system measured is equal to the charge state corresponding to the second operating point, the operating point being once again displaced to the first operating point;
a second step of modification of the operating point of the system during which the operating point is displaced from the first operating point to the second operating point, the modification of the operating point taking place adiabatically during the passage of the avoided crossing such that, during said second step, the system transits from the first charge state (1,1) to the charge state corresponding to the second operating point when the two charged particles contained in the system are in the second spin state T+ and is maintained in the first charge state (1,1) for the other spin states;
a second step of measuring the charge state of the system, the spin state of the two charged particles at the first operating point being the second spin state T+ if the charge state of the system measured is equal to the charge state corresponding to the second operating point, the operating point being once again displaced to the first operating point;
a third step of modification of the operating point of the system during which the operating point is displaced from the first operating point to the second operating point, the modification of the operating point taking place non-adiabatically during the passage of the avoided crossing;
a waiting step at a waiting operating point corresponding to a charge state identical to that of the second operating point during a predefined time, step during which the system transits from the first charge state (1,1) to the charge state corresponding to the second operating point when the two charged particles are in the third spin state T0 and is maintained in the first charge state for the fourth spin state T−;
a third step of measuring the charge state of the system, the spin state of the two particles at the first operating point being the third spin state T0 if the charge state of the system measured is equal to the charge state corresponding to the second operating point and the fourth spin state T− if the charge state of the system measured is equal to the first charge state.
2. The method according to claim 1 , wherein the waiting operating point is different from the second operating point, the method comprising, before the waiting step, a step of displacement of the operating point from the second operating point to the waiting operating point.
3. The method according to claim 1 , wherein each step of modification of the operating point from the first operating point to the second operating point comprises:
a sub-step of modification from the first operating point to an intermediate operating point, the intermediate operating point corresponding to the first charge state of the system, the avoided crossing formed by the first spin state S and the second spin state T+ being crossed during this sub-step;
a sub-step of modification from the intermediate operating point to the second operating point, the modification taking place non-adiabatically during this sub-step.
4. The method according to claim 1 , wherein each step of measuring the charge state is preceded by a step of displacement of the operating point from the second operating point or from the waiting operating point to a fourth operating point corresponding to a charge state identical to the second operating point and having a value of the first parameter Γ such that:
Γ
⪡
1
τ
mes
where τ mes is the time constant associated with the measurement of the charge state of the system.
5. A quantum device comprising at least two quantum dots and a system configured to implement the method according to claim 1 .
6. A non-transitory computer readable data support, on which is recorded a computer programme comprising instructions which, when the programme is executed on a processor lead it to implement the method according to claim 1 .
7. A method for determining a fidelity of a measurement of a first spin state noted S of two charged particles being able to adopt said first spin state S, a second spin state noted T+, a third spin state noted T0 and a fourth spin state noted T−, the two charged particles being contained in a system, comprising a first quantum dot and a second quantum dot and characterised by a first parameter Γ relative to a potential barrier separating the first and second quantum dots and a second parameter ε corresponding to a difference in energy between a fundamental state of the first quantum dot and a fundamental state of the second quantum dot, a couple formed by values of the first and second parameters defining an operating point of the system as a function of which the system can adopt a first charge state noted (1,1) wherein each quantum dot contains a charged particle, a second charge state noted (2,0) wherein the first quantum dot contains two charged particles and a third charge state noted (0,2) wherein the second quantum dot contains two charged particles, an operating point of the system being initially in a first operating point corresponding to the first charge state (1,1) of the system and for which the first S, second T+, third T0 and fourth T− spin states are eigenstates of the spin of the two charged particles, the method comprising, for an initial population of spin states wherein the first spin state S is in the majority:
a step of modification of the operating point of the system during which the operating point is displaced from the first operating point to a second operating point corresponding to the second charge state (2,0) or to the third charge state (0,2), the energy level of the first spin state S and the second spin state T+ forming an avoided crossing during the displacement from the first operating point to the second operating point, the modification of the operating point comprising a predetermined number of non-adiabatic transitions back and forth on either side of the avoided crossing;
a step of measuring the charge state of the system;
the steps being repeated from the same population of spin states for a plurality of numbers of transitions back and forth, the fidelity being determined from an evolution of the probability of measurement of a charge state corresponding to the second operating point as a function of the number of transitions back and forth.
8. A method for determining a fidelity of the measurement of a second spin state noted T+ of two charged particles being able to adopt a first spin state S, the second spin state noted T+, a third spin state noted T0 and a fourth spin state noted T−, the two charged particles being contained in a system, comprising a first quantum dot and a second quantum dot and characterised by a first parameter Γ relative to a potential barrier separating the first and second quantum dots and a second parameter ε corresponding to a difference in energy between a fundamental state of the first quantum dot and a fundamental state of the second quantum dot, the couple formed by the values of these two parameters defining an operating point of the system as a function of which the system can adopt a first charge state noted (1,1) wherein each quantum dot contains a charged particle, a second charge state noted (2,0) wherein the first quantum dot contains two charged particles and a third charge state noted (0,2) wherein the second quantum dot contains two charged particles, the operating point of the system being initially in a first operating point corresponding to the first charge state (1,1) of the system and for which the first S, second T+, third T0 and fourth T− spin states are eigenstates of the spin of the two charged particles, the method comprising, for an initial population of spin states wherein the second spin state T+ is in the majority:
a step of modification of the operating point of the system during which the operating point is displaced from the first operating point to a second operating point corresponding to the second charge state (2,0) or to the third charge state (0,2), the energy level of the first spin state S and the second spin state T+ forming an avoided crossing during the displacement from the first operating point to the second operating point, the modification of the operating point comprising a predetermined number of adiabatic transitions back and forth on either side of the avoided crossing;
a step of measuring the charge state of the system;
the steps being repeated from the same population of spin states for a plurality of numbers of transitions back and forth, the fidelity being determined from the evolution of the probability of measurement of a charge state corresponding to the second operating point as a function of the number of transitions back and forth.
9. A method for determining a fidelity of the measurement of a third spin state noted T0 of two charged particles being able to adopt a first spin state S, a second spin state noted T+, the third spin state noted T0 and a fourth spin state noted T−, the two charged particles being contained in a system, comprising a first quantum dot and a second quantum dot and characterised by a first parameter Γ relative to the potential barrier separating the first and second quantum dots and a second parameter ε corresponding to the difference in energy between the fundamental state of the first quantum dot and the fundamental state of the second quantum dot, a couple formed by values of the first and second parameters defining an operating point of the system as a function of which the system can adopt a first charge state noted (1,1) wherein each quantum dot contains a charged particle, a second charge state noted (2,0) wherein the first quantum dot contains two charged particles and a third charge state noted (0,2) wherein the second quantum dot contains two charged particles, an operating point of the system being initially in a first operating point corresponding to the first charge state (1,1) of the system and for which the first S, second T+, third T0 and fourth T− spin states are eigenstates of the spin of the two charged particles, the method comprising, for an initial population of spin states wherein the third spin state T0 is in the majority:
a step of modification of the operating point of the system during which the operating point is displaced from the first operating point to a second operating point corresponding to the second charge state (2,0) or to the third charge state (0,2), the energy level of the first spin state S and the second spin state T+ forming an avoided crossing during the displacement from the first operating point to the second operating point, the modification of the operating point taking place non-adiabatically during the passage of the avoided crossing;
a waiting step at a waiting operating point corresponding to a charge state identical to that of the second operating point during a predefined time;
a step of measuring the charge state of the system;
the steps being repeated from the same population of spin states for a plurality of predefined waiting times, the fidelity being determined from the evolution of the probability of measurement of a charge state corresponding to the second operating point as a function of the waiting times.