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High Resolution non-Markovianity in NMR

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ABSTRACT

Memoryless time evolutions are ubiquitous in nature but often correspond to a resolution-induced approximation, i.e. there are correlations in time whose effects are undetectable. Recent advances in the dynamical control of small quantum systems provide the ideal scenario to probe some of these effects. Here we experimentally demonstrate the precise induction of memory effects on the evolution of a quantum coin (qubit) by correlations engineered in its environment. In particular, we design a collisional model in Nuclear Magnetic Resonance (NMR) and precisely control the strength of the effects by changing the degree of correlation in the environment and its time of interaction with the qubit. We also show how these effects can be hidden by the limited resolution of the measurements performed on the qubit. The experiment reinforces NMR as a test bed for the study of open quantum systems and the simulation of their classical counterparts.

No MeSH data available.


Quantum circuit representing the NMR pulse sequence for the state preparation of the initial state of system and environment given by ρ(0) ⊗ ρenv.The boxes with the symbols Rα(θ) indicate that a rotation of the angle θ on that particular spin was performed around the α direction and . The boxes with the symbol τ2 represent a free evolution of the system and environment for a period of time τ2. The box with the symbol Grad stands for the magnetic field gradient that is applied in the z-direction.
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f6: Quantum circuit representing the NMR pulse sequence for the state preparation of the initial state of system and environment given by ρ(0) ⊗ ρenv.The boxes with the symbols Rα(θ) indicate that a rotation of the angle θ on that particular spin was performed around the α direction and . The boxes with the symbol τ2 represent a free evolution of the system and environment for a period of time τ2. The box with the symbol Grad stands for the magnetic field gradient that is applied in the z-direction.

Mentions: For the experiment, the values of η were very small and this created a huge source of errors in the operations, since they had to be performed in tiny steps and, therefore, were not so different. In fact, the rotations angles were so small that the controlled operations, which simulate the collisions, were very hard to be performed properly. In order to achieve the necessary precision in the experiment the rotations of θ had to be precisely adjusted for each value of η of the specific collision. For adjusting the angles values, two parameters may be varied, the amplitude and duration of the radio frequency pulses. However, varying these two parameters the sequence of operations needed for the corrections changes as well. Therefore, the correct pulse sequences were determined by combining the two analysis and testing in the spectrometer. A good precision could be achieved then and the small rotations, of the order of 0.30 degrees, could be implemented. For the state preparation the pulse sequence shown in Fig. 6 was performed, for more details see refs 36 and 37. The time τ2 of the free evolution here is related to the correlation parameter q as it is presented in Fig. 7. A the end of the circuit a magnetic field gradient in the z-direction is applied, which works as a transversal relaxation time killing the off-diagonal terms of the density matrix of system and environment. Finally, after each run, full state tomography was performed in the state of the system34.


High Resolution non-Markovianity in NMR
Quantum circuit representing the NMR pulse sequence for the state preparation of the initial state of system and environment given by ρ(0) ⊗ ρenv.The boxes with the symbols Rα(θ) indicate that a rotation of the angle θ on that particular spin was performed around the α direction and . The boxes with the symbol τ2 represent a free evolution of the system and environment for a period of time τ2. The box with the symbol Grad stands for the magnetic field gradient that is applied in the z-direction.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5037399&req=5

f6: Quantum circuit representing the NMR pulse sequence for the state preparation of the initial state of system and environment given by ρ(0) ⊗ ρenv.The boxes with the symbols Rα(θ) indicate that a rotation of the angle θ on that particular spin was performed around the α direction and . The boxes with the symbol τ2 represent a free evolution of the system and environment for a period of time τ2. The box with the symbol Grad stands for the magnetic field gradient that is applied in the z-direction.
Mentions: For the experiment, the values of η were very small and this created a huge source of errors in the operations, since they had to be performed in tiny steps and, therefore, were not so different. In fact, the rotations angles were so small that the controlled operations, which simulate the collisions, were very hard to be performed properly. In order to achieve the necessary precision in the experiment the rotations of θ had to be precisely adjusted for each value of η of the specific collision. For adjusting the angles values, two parameters may be varied, the amplitude and duration of the radio frequency pulses. However, varying these two parameters the sequence of operations needed for the corrections changes as well. Therefore, the correct pulse sequences were determined by combining the two analysis and testing in the spectrometer. A good precision could be achieved then and the small rotations, of the order of 0.30 degrees, could be implemented. For the state preparation the pulse sequence shown in Fig. 6 was performed, for more details see refs 36 and 37. The time τ2 of the free evolution here is related to the correlation parameter q as it is presented in Fig. 7. A the end of the circuit a magnetic field gradient in the z-direction is applied, which works as a transversal relaxation time killing the off-diagonal terms of the density matrix of system and environment. Finally, after each run, full state tomography was performed in the state of the system34.

View Article: PubMed Central - PubMed

ABSTRACT

Memoryless time evolutions are ubiquitous in nature but often correspond to a resolution-induced approximation, i.e. there are correlations in time whose effects are undetectable. Recent advances in the dynamical control of small quantum systems provide the ideal scenario to probe some of these effects. Here we experimentally demonstrate the precise induction of memory effects on the evolution of a quantum coin (qubit) by correlations engineered in its environment. In particular, we design a collisional model in Nuclear Magnetic Resonance (NMR) and precisely control the strength of the effects by changing the degree of correlation in the environment and its time of interaction with the qubit. We also show how these effects can be hidden by the limited resolution of the measurements performed on the qubit. The experiment reinforces NMR as a test bed for the study of open quantum systems and the simulation of their classical counterparts.

No MeSH data available.