Quantum control and semiclassical quantumgravity Lajos Di´ osi Wigner Centre, Budapest 9 Apr 2019, Evanston IL 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 9 Apr 2019, Evanston IL 1 / 19
Abstract 1 Semiclassical thought-experiment 1986 2 Fragments from history 3 Semiclassical Gravity 1962-63: sharp metric 4 Sharp metric Newtonian limit Testing self-attraction Interaction generated “on phone line” 5 Quantum control to generate potential (tutorial) Quantum control to generate potential (summary) 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 9 Apr 2019, Evanston IL 2 / 19
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 9 Apr 2019, Evanston IL 3 / 19
Semiclassical thought-experiment 1986 1. electromagnetism quantized, confirmed by tests 2. nuclear forces unified by the Standard Model 3. weak forces 4. gravity (space-time) either quantized or not, no tests so far Is it sharp or uncertain (fluctuating)? If it is fluctuating, what is the spectrum of fluctuations δ g ab ? 1986: Newtonian limit δ g 00 = δ Φ , thought-experiment with quantized probe + classical Φ , order of magnitude estimate: � G � δ Φ t ( r ) δ Φ s ( y ) � stoch = const × | x − y | δ ( t − s ) ⇒ DP positional decoherence for massive objects, testable in the lab? Can’t we get rid of the order-of-magnitude estimate 1986 ? 2016-17: We can (Tilloy & D). Lajos Di´ osi (Wigner Centre, Budapest) Quantum control and semiclassical quantumgravity 9 Apr 2019, Evanston IL 4 / 19
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 9 Apr 2019, Evanston IL 5 / 19
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 9 Apr 2019, Evanston IL 6 / 19
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 9 Apr 2019, Evanston IL 7 / 19
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 9 Apr 2019, Evanston IL 8 / 19
Interaction generated “on phone line” Alice Bob spring M A ///////// V ( x A − x B ) ///////// M B at x A at x B We can replace the spring by a phone line + two local springs under local control of Alice and Bob, resp.: phone line Alice − − − to communicate − − − Bob x A → B , A ← x B ց ւ M A /// | | /// M B Trivial classically, non-trivial in quantum. Lajos Di´ osi (Wigner Centre, Budapest) Quantum control and semiclassical quantumgravity 9 Apr 2019, Evanston IL 9 / 19
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 quantumgravity9 Apr 2019, Evanston IL 10 / 19
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 quantumgravity9 Apr 2019, Evanston IL 11 / 19
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 quantumgravity9 Apr 2019, Evanston IL 12 / 19
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 quantumgravity9 Apr 2019, Evanston IL 13 / 19
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