Quantum control and semiclassical quantumgravity Lajos Di osi - PowerPoint PPT Presentation

Quantum control and semiclassical quantumgravity Lajos Di´ osi Wigner Centre, Budapest 23 Nov 2018, Wigner RCP National Research Development and Innovation Office Projects 2017-1.2.1-NKP-2017-00001 and K12435 EU COST Action CA15220 ‘Quantum Technologies in Space’ Lajos Di´ osi (Wigner Centre, Budapest) Quantum control and semiclassical quantumgravity 23 Nov 2018, Wigner RCP 1 / 17

Abstract 1 Fragments from history 2 Semiclassical Gravity 1962-63: sharp metric 3 Sharp metric Newtonian limit Testing self-attraction Quantum control to generate potential (tutorial) 4 Quantum control to generate potential (summary) 5 Decoherent Semiclassical Gravity: unsharp metric 6 Unsharp metric Newtian limit ... coincides with DP wavefunction collapse theory Testing DP: LISA Pathfinder MAQRO Summary 7 Decoherent Semiclassical Gravity wouldn’t have been realized 8 without ... References 9 Lajos Di´ osi (Wigner Centre, Budapest) Quantum control and semiclassical quantumgravity 23 Nov 2018, Wigner RCP 2 / 17

Abstract Quantum gravity has not yet obtained a usable theory. We apply the semiclassical theory instead, where the space-time remains classical (i.e.: unquantized). However, the hybrid quantum-classical coupling is acausal, violates both the linearity of quantum theory and the Born rule as well. Such anomalies can go away if we modify the standard mean-field coupling, building on the mechanism of quantum measurement and feed-back well-known in, e.g., quantum optics. The newtonian limit can fully be worked out, it leads to the gravity-related spontaneous wave function collapse theory of Penrose and the speaker. Lajos Di´ osi (Wigner Centre, Budapest) Quantum control and semiclassical quantumgravity 23 Nov 2018, Wigner RCP 3 / 17

Fragments from history Bronstein (1935): A sharp space-time structure is unob- servable (because of Schwartzschild radii of test bodies). Quantization of gravity can not copy quantization of elec- tromagnetism. We may be enforced to reject our ordinary concept of space-time. 1906-1938 J´ anossy (1952): Quantum mechanics should be more clas- sical. Expansion of the wave packet might be limited by ˙ 2 M ψ ′′ ( x ) − γ ( x − � x � ) 2 ψ ( x ) + 1 i � 2 γ (∆ x ) 2 ψ ( x ) ψ ( x ) = if we accept superluminality caused by the nonlinear term. 1912-1978 K´ arolyh´ azy (1966): The ultimate unsharpness of space-time structure limits coherent expansion of massive objects’ po- sition (while individual particles can expand coherently with no practical limitations). 1929-2012 Lajos Di´ osi (Wigner Centre, Budapest) Quantum control and semiclassical quantumgravity 23 Nov 2018, Wigner RCP 4 / 17

Semiclassical Gravity 1962-63: sharp metric Sharp classical space-time metric (Møller, Rosenfeld 1962-63): G ab = 8 π G c 4 � Ψ | ˆ T ab | Ψ � Schrödinger equation on background metric g : Ψ � = − i | ˙ ˆ H [ g ] | Ψ � � That’s our powerful effective hybrid dynamics for ( g ab , | Ψ � ) , but with fundamental anomalies (superluminality, no Born rule, ...) that are unrelated to relativity and even gravitation just related to quantum-classical coupling that makes Schrödinger eq. nonlinear No deterministic hybrid dynamics is correct fundamentally! Way out: metric cannot be sharp, must have fluctuations δ g ab . Lajos Di´ osi (Wigner Centre, Budapest) Quantum control and semiclassical quantumgravity 23 Nov 2018, Wigner RCP 5 / 17

Sharp metric Newtonian limit G 00 = 8 π Gc − 4 � Ψ | ˆ T 00 | Ψ � ⇒ ∆Φ = 4 π G � Ψ | ˆ ̺ | Ψ � � ˆ � ˙ ˙ | Ψ � = − ( i / � )ˆ � ˆ H [ g ] | Ψ � ⇒ | Ψ � = − ( i / � ) H 0 + ̺ Φ dV | Ψ � ⇒ ⇒ Schrödinger-Newton Equation with self-attraction: � � ˆ � � ̺ ( x ) � Ψ | ˆ ̺ ( y ) | Ψ � | Ψ � = − i ˙ ˆ H 0 − G | Ψ � d x d y � | x − y | Single “pointlike” body c.o.m. motion: � | ψ ( y ) | 2 d y ψ ( x ) = i � 2 M ∇ 2 ψ ( x ) + i ˙ � GM 2 | x − y | ψ ( x ) � �� � self-attraction Solitonic solutions: ∆ x ∼ � 2 / GM 3 . Irrelevant for atomic M , grow relevant for nano- M : M ∼ 10 − 15 g , ∆ x ∼ 10 − 5 cm That’s quantumgravity in the lab [D. 1984]. Lajos Di´ osi (Wigner Centre, Budapest) Quantum control and semiclassical quantumgravity 23 Nov 2018, Wigner RCP 6 / 17

Testing self-attraction Schrödinger-Newton Equation for 1 D motion of a Massive oscillator: ψ ( x ) = i � 2 M ψ ′′ ( x ) − iM � G ( x − � x � ) 2 � Ω 2 x 2 + ω 2 ˙ ψ ( x ) 2 � ω 2 G = const. × G × nuclear density in M Lajos Di´ osi (Wigner Centre, Budapest) Quantum control and semiclassical quantumgravity 23 Nov 2018, Wigner RCP 7 / 17

Quantum control to generate potential (tutorial) Sequential measurements of ˆ x plus feedback: measurement unitary measurement unitary of x evolution of x evolution . . . | > M U | > M U | > ψ ψ ψ 1 2 0 1 2 feedback feedback outcome x 1 outcome x 2 At ∞ repetition frequency: time-continuous monitoring+feedback. = γ − 1 = � Ψ t | ˆ x | Ψ t � + δ x t E δ x t δ x s δ ( t − s ) x t ���� ���� � �� � ���� � �� � signal mean noise correlation γ = precision To generate a potential, take ˆ H fb ( t ) = Rx t ˆ x = R ( � Ψ t | ˆ x | Ψ t � + δ x t )ˆ x . | Ψ � = − i ˙ � (ˆ H 0 + 1 x 2 ) | Ψ �− 1 8 [ γ + 4 γ − 1 ( R / � ) 2 x � ) 2 2 R ˆ ] (ˆ x −� ˆ | Ψ � + . . . δ x | Ψ � � �� � � �� � � �� � � �� � stochastic to be minimized localisation fb − generated ρ = − i ρ ] − 1 ˙ � [ˆ H 0 + 1 x 2 , ˆ ˆ 2 R ˆ 2 � R [ˆ x , [ˆ x , ˆ ρ ]] Lajos Di´ osi (Wigner Centre, Budapest) Quantum control and semiclassical quantumgravity 23 Nov 2018, Wigner RCP 8 / 17

Quantum control to generate potential (summary) Assume ˆ x is being monitored, yielding signal x t = � Ψ t | ˆ x | Ψ t � + δ x t . Apply feedback via the hybrid Hamiltonian ˆ H fb ( t ) = Rx t ˆ x = R � ˆ x � t ˆ x + R δ x t ˆ x � �� � � �� � ( white ) noise part of coupling sharp semiclassical coupling Sharp+noisy terms together cancel nonlinearity (and related anomalies) from the quantum dynamics: ρ = − i ρ ] − 1 ˙ � [ˆ H 0 + 1 x 2 , ˆ ˆ 2 R ˆ 2 � R [ˆ x , [ˆ x , ˆ ρ ]] New potential has been generated ‘semiclassically’ and consistently with quantum mechanics, but at the price of decoherence. Lajos Di´ osi (Wigner Centre, Budapest) Quantum control and semiclassical quantumgravity 23 Nov 2018, Wigner RCP 9 / 17

Decoherent Semiclassical Gravity: unsharp metric Assume ˆ T ab is spontaneously measured (monitored) Let T ab be the measured value (called signal in control theory) Replace Møller-Rosenfeld 1962-63 by G ab = 8 π G c 4 T ab = 8 π G c 4 ( � ˆ T ab � + δ T ab ) i.e.: source Einstein eq. by the noisy signal (meanfield+noise) For backaction of monitoring, add terms to Schrödinger eq.: dt | Ψ � = − i d ˆ H [ g ] | Ψ � + nonlinear + stoch . terms � Tune precision of monitoring by Principle of Least Decoherence D 1990, Kafri, Taylor & Milburn 2014, Tilloy & D 2016-17 Lajos Di´ osi (Wigner Centre, Budapest) Quantum control and semiclassical quantumgravity 23 Nov 2018, Wigner RCP 10 / 17

Unsharp metric Newtonian limit Assume ˆ ̺ is spontaneously measured (monitored) Let ̺ t be the measured value (called signal in control theory) Source classical Newtonian gravity by the signal: � d y Φ t ( x ) = − G | x − y | ̺ t ( y ) Introduce ˆ � ˆ H fb = ̺ Φ dV to induce Newton interaction For backaction of monitoring, add terms to Schrödinger eq.: dt | Ψ � = − i d ˆ H 0 | Ψ � + nonlinear + stoch . terms � Tune precision of monitoring by Principle of Least Decoherence Such theory of unsharp semiclassical gravity coincides with ... Lajos Di´ osi (Wigner Centre, Budapest) Quantum control and semiclassical quantumgravity 23 Nov 2018, Wigner RCP 11 / 17

... coincides with DP wavefunction collapse theory Unique ultimate unsharpness of Newton potential Φ (metric): � G E δ Φ t ( r ) δ Φ s ( y )= 2 | x − y | δ ( t − s ) By averaging over the stochastic Φ (metric), master eq. (D. 1986):   � d x d y � d x d y   d ˆ ρ � � dt = − i H 0 + G  − G  ˆ  | x − y | ˆ ̺ ( x )ˆ ̺ ( y ) , ˆ ρ | x − y | [ˆ ̺ ( x ) , [ˆ ̺ ( y ) , ˆ ρ ]]   2 2 � �    � �� � � �� � Newton pairpotential DP decoherence Double merit: Semiclassical theory of gravity, a hybrid dynamics of (Φ , | Ψ � ) free of anomalies (no superluminality, valid Born rule). Theory of G-related spontaneous collapse (Schrödinger’s Cats go collapsed). Lajos Di´ osi (Wigner Centre, Budapest) Quantum control and semiclassical quantumgravity 23 Nov 2018, Wigner RCP 12 / 17

Testing DP: LISA Pathfinder Lajos Di´ osi (Wigner Centre, Budapest) Quantum control and semiclassical quantumgravity 23 Nov 2018, Wigner RCP 13 / 17