On the WEAK MEASUREMENT of the ELECTRICAL THz CURRENT: a NEW SOURCE - PowerPoint PPT Presentation

2015, July 17 th UPoN 2015 On the WEAK MEASUREMENT of the ELECTRICAL THz CURRENT: a NEW SOURCE of NOISE? Damiano Marian 1 , Nino Zangh` ı 2 , Xavier Oriols 1 1 Autonomous University of Barcelona 2 University of Genoa Barcelona - 2015, July 17 th Damiano Marian 1 / 23

Index 1 Open problem Barcelona - 2015, July 17 th Damiano Marian 2 / 23

Index 1 Open problem 2 Novel approach to model the measurement of THz current Barcelona - 2015, July 17 th Damiano Marian 2 / 23

Index 1 Open problem 2 Novel approach to model the measurement of THz current 3 New source of noise Barcelona - 2015, July 17 th Damiano Marian 2 / 23

Index 1 Open problem 2 Novel approach to model the measurement of THz current 3 New source of noise 4 Measurement of the local (Bohmian) velocities Barcelona - 2015, July 17 th Damiano Marian 2 / 23

Index 1 Open problem 2 Novel approach to model the measurement of THz current 3 New source of noise 4 Measurement of the local (Bohmian) velocities 5 Concluding Remarks Barcelona - 2015, July 17 th Damiano Marian 2 / 23

Index 1 Open problem 2 Novel approach to model the measurement of THz current 3 New source of noise 4 Measurement of the local (Bohmian) velocities 5 Concluding Remarks Barcelona - 2015, July 17 th Damiano Marian 3 / 23

1 - Open problem How do we model the measurement of the high frequency current? Barcelona - 2015, July 17 th Damiano Marian 4 / 23

1 - Open problem How do we model the measurement of the high frequency current? Year 2015 2020 2025 ⇒ Cutoff Frequency (GHz) 620 1137 2062 International Technology Roadmap for Semiconductors (2011) Barcelona - 2015, July 17 th Damiano Marian 4 / 23

1 - Open problem How do we model the measurement of the high frequency current? Year 2015 2020 2025 ⇒ Cutoff Frequency (GHz) 620 1137 2062 International Technology Roadmap for Semiconductors (2011) ⇒ Total Current = Particle + Displacement Current S i ǫ ( r ) d E ( r , t ) � I d ( t ) = · d s dt Barcelona - 2015, July 17 th Damiano Marian 4 / 23

1 - Open problem How do we model the measurement of the high frequency current? Year 2015 2020 2025 ⇒ Cutoff Frequency (GHz) 620 1137 2062 International Technology Roadmap for Semiconductors (2011) ⇒ Total Current = Particle + Displacement Current S i ǫ ( r ) d E ( r , t ) � I d ( t ) = · d s dt ⇒ Continuous (or very High Frequency) Measurement ⇓ Inclusion of the Back-Action (Disturbance of quantum system) Barcelona - 2015, July 17 th Damiano Marian 4 / 23

1 - Open problem How is Measurement modelled in Quantum Mechanics? Barcelona - 2015, July 17 th Damiano Marian 5 / 23

1 - Open problem How is Measurement modelled in Quantum Mechanics? Strong Ini tj al Wave Func tj on J. Von Neumann: PUP (1955) Barcelona - 2015, July 17 th Damiano Marian 5 / 23

1 - Open problem How is Measurement modelled in Quantum Mechanics? Strong S ts ong Opera tp r Ini tj al Wave Func tj on J. Von Neumann: PUP (1955) Barcelona - 2015, July 17 th Damiano Marian 5 / 23

1 - Open problem How is Measurement modelled in Quantum Mechanics? Strong Wave Func tj on af tf r S ts ong Measurement J. Von Neumann: PUP (1955) Barcelona - 2015, July 17 th Damiano Marian 5 / 23

1 - Open problem How is Measurement modelled in Quantum Mechanics? Strong Weak Wave Func tj on af tf r S ts ong Measurement Ini tj al Wave Func tj on Y. Aharonov, D. Z. Albert, and L. Vaidman: PRL (1988) J. Von Neumann: PUP (1955) Barcelona - 2015, July 17 th Damiano Marian 5 / 23

1 - Open problem How is Measurement modelled in Quantum Mechanics? Strong Weak Weak Opera tp r Wave Func tj on af tf r S ts ong Measurement Ini tj al Wave Func tj on Y. Aharonov, D. Z. Albert, and L. Vaidman: PRL (1988) J. Von Neumann: PUP (1955) Barcelona - 2015, July 17 th Damiano Marian 5 / 23

1 - Open problem How is Measurement modelled in Quantum Mechanics? Strong Weak Wave Func tj on af tf r S ts ong Measurement Wave Func tj on af tf r Weak Measurement Y. Aharonov, D. Z. Albert, and L. Vaidman: PRL (1988) J. Von Neumann: PUP (1955) Barcelona - 2015, July 17 th Damiano Marian 5 / 23

1 - Open problem How is Measurement modelled in Quantum Mechanics? Weak Wave Func tj on af tf r Weak Measurement Main features of the Weak Measurement � I � strong = � I � weak Wave Function of the system is slightly perturbed after the interaction Y. Aharonov, D. Z. Albert, and L. Vaidman: PRL (1988) Barcelona - 2015, July 17 th Damiano Marian 5 / 23

1 - Open problem Measuring the current at high frequency Three ways: I Taking information from the system without worrying about the apparatus → Be careful! Barcelona - 2015, July 17 th Damiano Marian 6 / 23

1 - Open problem Measuring the current at high frequency Three ways: I Taking information from the system without worrying about the apparatus → Be careful! II Looking for an Operator...but... Barcelona - 2015, July 17 th Damiano Marian 6 / 23

1 - Open problem Measuring the current at high frequency Three ways: I Taking information from the system without worrying about the apparatus → Be careful! II Looking for an Operator...but... Which is the operator that defines the (non-unitary) evolution of the wave function when measuring the total current? Barcelona - 2015, July 17 th Damiano Marian 6 / 23

1 - Open problem Measuring the current at high frequency Three ways: I Taking information from the system without worrying about the apparatus → Be careful! II Looking for an Operator...but... Which is the operator that defines the (non-unitary) evolution of the wave function when measuring the total current? Is it “continuous” or “instantaneous”? Does it provide a “weak” or a “strong” perturbation on the wave function? Barcelona - 2015, July 17 th Damiano Marian 6 / 23

1 - Open problem Measuring the current at high frequency Three ways: I Taking information from the system without worrying about the apparatus → Be careful! II Looking for an Operator...but... Which is the operator that defines the (non-unitary) evolution of the wave function when measuring the total current? Is it “continuous” or “instantaneous”? Does it provide a “weak” or a “strong” perturbation on the wave function? III Looking at the problem from a different point of view Barcelona - 2015, July 17 th Damiano Marian 6 / 23

1 - Open problem Measuring the current at high frequency Three ways: I Taking information from the system without worrying about the apparatus → Be careful! II Looking for an Operator...but... Which is the operator that defines the (non-unitary) evolution of the wave function when measuring the total current? Is it “continuous” or “instantaneous”? Does it provide a “weak” or a “strong” perturbation on the wave function? III Looking at the problem from a different point of view Include the apparatus and see what happens! Barcelona - 2015, July 17 th Damiano Marian 6 / 23

1 - Open problem Measuring the current at high frequency Three ways: I Taking information from the system without worrying about the apparatus → Be careful! II Looking for an Operator...but... Which is the operator that defines the (non-unitary) evolution of the wave function when measuring the total current? Is it “continuous” or “instantaneous”? Does it provide a “weak” or a “strong” perturbation on the wave function? III Looking at the problem from a different point of view Include the apparatus and see what happens! Electron X(t) Ammeter Cable Pointer (t) 𝚶 V z S A x S i y Device Active Region Barcelona - 2015, July 17 th Damiano Marian 6 / 23

Index 1 Open problem 2 Novel approach to model the measurement of THz current 3 New source of noise 4 Measurement of the local (Bohmian) velocities 5 Concluding Remarks Barcelona - 2015, July 17 th Damiano Marian 7 / 23

2 - Approach to model the measurement of THz current Many-Body Problem i � ∂ Ψ( x 1 , x 2 , ..., x N , t ) = [ H 0 + V Coul ] Ψ( x 1 , x 2 , ..., x N , t ) ∂ t Barcelona - 2015, July 17 th Damiano Marian 8 / 23

2 - Approach to model the measurement of THz current Many-Body Problem i � ∂ Ψ( x 1 , x 2 , ..., x N , t ) = [ H 0 + V Coul ] Ψ( x 1 , x 2 , ..., x N , t ) ∂ t Coulomb Interaction ↓ N q i q j 1 1 √ V Coul = � 4 πǫ ( r ) 2 ( x i − x j ) 2 i =1 , j � = i Barcelona - 2015, July 17 th Damiano Marian 8 / 23

2 - Approach to model the measurement of THz current Many-Body Problem i � ∂ Ψ( x 1 , x 2 , ..., x N , t ) = [ H 0 + V Coul ] Ψ( x 1 , x 2 , ..., x N , t ) ∂ t Coulomb Interaction ↓ N q i q j 1 1 √ V Coul = � 4 πǫ ( r ) 2 ( x i − x j ) 2 i =1 , j � = i Many Particle ↓ Numerically inaccessible Barcelona - 2015, July 17 th Damiano Marian 8 / 23

2 - Approach to model the measurement of THz current Conditional Wave Function i � ∂ψ ( x 1 , t ) dX 1 ( t ) � ∇ ψ � = � = [ H 0 + V Cond ] ψ ( x 1 , t ) m Im ∂ t dt ψ D. D¨ urr, S. Goldstein, and N. Zangh` ı: JSP (1992;2005) Barcelona - 2015, July 17 th Damiano Marian 9 / 23